Previous Year Question Papers Archives

Ans: We are given the refractive index of glass to be, $\mu=1.5$ BreWster angle $=\theta$ Brewster angle is known to be related to refractive index as: $$ \begin{array}{l} \tan \theta=\mu \\...

At a certain location in Africa, a compass points $12^{\circ}$ west of the geographic north. The north tip of the magnetic needle of a dip circle placed in the plane of magnetic meridian points above the horizontal. The horizontal component of the earth’s field is measured to be $0.16 \mathrm{G} .$ Specify the direction and magnitude of the earth’s field at the location.At a certain location in Africa, a compass points $12^{\circ}$ west of the geographic north. The north tip of the magnetic needle of a dip circle placed in the plane of magnetic meridian points above the horizontal. The horizontal component of the earth’s field is measured to be $0.16 \mathrm{G} .$ Specify the direction and magnitude of the earth’s field at the location.

Ans: In the above question it is given that: Angle of declination, $\theta=12^{\circ}$ Angle of dip, $\delta=60^{\circ}$ Horizontal component of earth's magnetic field, $B_{H}=0.16 \mathrm{G}$...

Two long and parallel straight wires $A$ and $B$ carrying currents of $8.0 A$ and $5.0 \mathrm{~A}$ in the same direction are separated by a distance of $4.0 \mathrm{~cm}$. Estimate the force on a $10 \mathrm{~cm}$ section of wire A.

Ans: We are given the following: Current flowing in wire $A_{1} I_{A}=8.0 \mathrm{~A}$ Current flowing in wire $B, I_{B}=5.0 \mathrm{~A}$ Distance between the two wires, $r=4.0 \mathrm{~cm}=0.04...

A $3.0 \mathrm{~cm}$ wire carrying a current of $10 \mathrm{~A}$ is placed inside a solenoid perpendicular to its axis. The magnetic field inside the solenoid is given to be $0.27 \mathrm{~T}$. What is the magnetic force on the wire?

Ans: We are given the following: Length of the wire, $I=3 \mathrm{~cm}=0.03 \mathrm{~m}$ Current flowing in the wire, $1=10 \mathrm{~A}$. Magnetic field, $B=0.27 \mathrm{~T}$ Angle between the...

What is the magnitude of magnetic force per unit length on a wire carrying a current of $8 \mathrm{~A}$ and making an angle of $30^{\circ}$ with the direction of a uniform magnetic field of $0.15 \mathrm{~T} ?$

Ans: We are given the following: Current in the wire, $I=8 \mathrm{~A}$ Magnitude of the uniform magnetic field, $B=0.15 \mathrm{~T}$ Angle between the wire and magnetic field, $\theta=30^{\circ}$...

A long straight wire carries a current of $35 \mathrm{~A}$. What is the magnitude of the field $\mathrm{B}$ at a point $20 \mathrm{~cm}$ from the wire?

Ans: We are given the following: Current in the wire, $\mathrm{I}=35 \mathrm{~A}$ Distance of a point from the wire, $r=20 \mathrm{~cm}=0.2 \mathrm{~m}$ Magnitude of the magnetic field at this point...

State Biot-Savarts law. Derive an expression for magnetic field at the center of a circular coil of $n$-turns carrying current $-1$.

Ans: Biot - Savart law states that the magnetic field $\mathrm{dB}$ due to a current element dI at any point would be as following: $$ \begin{array}{l} \mathrm{dB} \propto \mathrm{dl} \\ \mathrm{dB}...

A straight wire carries a current of $10 \mathrm{~A}$. An electron moving at $10^{7} \mathrm{~m} / \mathrm{s}$ is at distance $2.0 \mathrm{~cm}$ from the wire. Find the force acting on the electron if its velocity is directed towards the wire.

Ans: We are given the current through the straight wire to be, $I=10 \mathrm{~A}$ Speed of the electron, $\mathrm{v}=10^{7} \mathrm{~m} / \mathrm{s}$ Distance of electron from the wire,...

Give one difference each between diamagnetic and ferromagnetic substances. Give one example of each.

Ans: Diamagnetic substances are the ones that are weakly repelled by a magnet. For example, gold. Ferromagnetic materials are the ones that are strongly attracted by a magnet. For example, iron.

A steady current flows in the network What will be the magnetic field at the center of the network?

Ans: The magnetic field at the center of the network is zero. This is because, magnetic field at the center of the loop would just equal and opposite $i . e .$, magnetic field due PQR is equal and...

A cyclotron is not suitable to accelerate electron. Why?

Ans: A cyclotron is not suitable to accelerate electron as its mass is known to be less due to which they gain speed and step out of the dee immediately,

Two wires of equal lengths are bent in the form of two loops. One of the loops is square shaped whereas the other loop is circular. These are suspended in a uniform magnetic field and the same current is passed through them. Which loop will experience greater torque? Give reasons.

Ans: We know the expression for torque as, $$ \begin{array}{l} \tau=\mathrm{NIAB} \\ \Rightarrow \tau \propto \mathrm{A} \end{array} $$ Since, we know that the area of circular loops is more than...

What will be the path of a charged particle moving along the direction of a uniform magnetic field?

Ans: The path of a charged particle moving along the direction of a uniform magnetic field would be a straight line path as no force would act on the particle.

State two properties of the material of the wire used for suspension of the coil in a moving coil galvanometer.

Ans: Two properties of the material of the wire used for suspension of the coil in a moving coil galvanometer are: i. Non-Brittle conductor ii. Restoring Torque per unit twist should be small.

V.I graph for a metallic wire at two different temperatures Which of these two temperatures is higher and why?

Ans: From the graph: Slope $=\frac{\mathrm{i}}{\mathrm{V}}$ It is known that, $\frac{i}{V}=\frac{1}{R}$ It means that the smaller the slope, the larger the resistance.

Two heated wires of the same dimensions are first connected in series and then it’s parallel to a source of supply. What will be the ratio of heat produced in the two cases?

Ans: It is known that, $$ \begin{array}{l} H=I^{2} R t \quad\left(I=\frac{V}{R}\right) \\ \Rightarrow H=\frac{V^{2}}{R^{2}} \times R \times t \\ \Rightarrow H=\frac{V^{2}}{R} t \\ \Rightarrow H...

Resistivities of copper, silver and manganin are $1.7 \times 10^{-8} \mathrm{~m}, 1.0 \times 10^{-8} \mathrm{~m}$ and $44 \times 10^{-8} \mathrm{~m}$ respectively which of these is the best conductor?

Ans: The resistance is directly proportional to specific resistance (resistivity), when length and area of cross-section is made constant. $R=\frac{\rho I}{A}$ Hence, silver is the best conductor as...

What is the work done in moving a $2 \mu \mathrm{C}$ point change from corner $A$ to corner $B$ of a square $A B C D$ when a $10 \mu C$ charge exists at the centre of the square?

Ans: Point $A \& B$ are at the same distance from the point $O$. Hence,

Why does the electric field inside a dielectric decrease when it is placed in an external electric field?

Ans: The electric field that is present inside a dielectric decreases when it is placed in an external electric field because of polarisation as it creates an internal electric field which is...

State Gauss’s Theorem in electrostatics? Using this theorem define an expression for the field intensity due to an infinite plane sheet of change of charge density $\sigma \mathrm{C} / \mathrm{m}^{2}$.

Ans: Gauss's Theorem has a statement that electric flux through a closed surface enclosing a charge $q$ in vacuum is $\frac{1}{\epsilon_{0}}$ times the magnitude of the charge enclosed $\mathrm{is}...

Prove that the energy stored in a parallel plate capacitor is given by $\frac{1}{2} \mathrm{CV}^{2}$

Physics, Previous Year Question Papers, RS Aggarwal Maths class 11 Differentiation

Ans: Let us suppose a capacitor is connected to a battery and it supplies a small amount of change dq at constant potential $V$, then a small amount of work done by the battery is given by $$...

Two dielectric slabs of dielectric constant $K_{1}$ and $K_{2}$ are filled in between the two plates, each of area A of the parallel plate capacitor as shown in the figure. Find the net capacitance of the capacitor? Area of each plate $\frac{A}{2}$

Ans: In the question, the two capacitors are in parallel Net Capacitance, $C=C_{1}+C_{2}$ $$ \begin{array}{l} \mathrm{C}_{1}=\frac{\mathrm{K}_{1}...

Describe schematically the equipotential surfaces corresponding to a) a constant electric field in the z-direction,

Ans: Equidistant planes which are parallel to the $x-y$ plane are the equipotential surfaces. b) a field that uniformly increases in magnitude but remains in a constant (say, z) direction, Ans:...

In a Van de Graaff type generator a spherical metal shell is to be a $15 \times 10^{6} \vee$ electrode. The dielectric strength of the gas surrounding the electrode is $5 \times 10^{7} \mathrm{Vm}^{-1}$. What is the minimum radius of the spherical shell required? (You will learn from this exercise why one cannot build an electrostatic generator using a very small shell which requires a small charge to acquire a high potential.)

Ans: Given that, Potential difference is given as, $V=15 \times 10^{6} \mathrm{~V}$ Dielectric strength of the surrounding gas $=5 \times 10^{\top} \mathrm{Vm}^{-1}$ Electric field intensity is...

Two charges $2 \mu \mathrm{C}$ and $-2 \mu \mathrm{C}$ are placed at points $A$ and $B 6 \mathrm{~cm}$ apart. a) Identify an equipotential surface of the system.

Ans: The situation is represented in the adjoining figure. An equipotential surface is the plane on which the total potential is zero everywhere. This plane is normal to line AB. The plane is...

The distance between the plates of a parallel plate capacitor is d. A metal plate of thickness $\left(\frac{d}{2}\right)$ is placed between the plates. What will be the effect on the capacitance?

Ans: For air $C_{0}=\frac{A \in_{0}}{d}$ Thickness $t=\frac{d}{2}$ only when $k=\infty$ $$ \begin{array}{l} C_{0}=\frac{A \in_{0}}{d} \\ C_{\text {mat }}=\frac{A \in_{0}}{(d-t)} \end{array} $$ $$...

A stream of electrons travelling with speed $\mathrm{vm} / \mathrm{s}$ at right angles to a uniform electric field $E$ is deflected in a circular path of radius $r .$ Prove that $\frac{e}{m}=\frac{v^{2}}{r E} ?$

Ans: The path of the electron that is travelling with velocity $\mathrm{vm} / \mathrm{s}$ at right angle of $\bar{E}$ is of circular shape. It requires a centripetal in nature, $F=\frac{m v^{2}}{r}$...

If the amount of electric flux entering and leaving a closed surface are $\phi_{1}$ and $\phi_{2}$ respectively. What is the electric charge inside the surface?

Ans: Net flux can be given as $=\phi_{2}-\phi_{1}$ Since $\phi=\frac{q}{\epsilon_{0}}$ $$ \Rightarrow \mathrm{Q}=\left(\phi_{2}-\phi_{1}\right) \in_{0} $$ The electric charge inside the surface can...

Draw one equipotential surfaces (1) Due to uniform electric field (2) For a point charge $(q<0) ?$

Ans: The diagrams are given as: Equipoterhibil Surfaces 3 $\mathrm{~ ( 2 c ) r o m}$

A parallel plate capacitor with air between the plates has a capacitance of 8pF $\left(1 \mathrm{pF}=10^{-12} \mathrm{~F}\right)$. What will be the capacitance if the distance between the plates is reduced by half and the space between them is filled with a substance of dielectric constant 6 ?

Ans: For air, capacitance can be expressed as, $C_{0}=\frac{A \in_{0}}{d}$ $$ C_{0}=8 \times p F=8 \times 10^{-12} F $$ Now $d^{\prime}=\frac{d}{2}$ and $K=6$ $$ \begin{array}{l} \Rightarrow...

Show mathematically that the potential at a point on the equatorial line of an electric dipole is Zero?

Ans: Electric potential at point on the equatorial line of an electric dipole can be expressed mathematically as: $$ \begin{array}{l} V=V_{P A}+V_{P B} \\ \Rightarrow...

What happens to the capacitance of a capacitor when a dielectric slab is placed between its plates?

Ans: The introduction of dielectric in a capacitor will reduce the effective charge on plate and therefore will increase the capacitance.

The plates of a charged capacitor are connected by a voltmeter. If the plates of the capacitor are moved further apart, what will be the effect on the reading of the voltmeter?

Ans: The relation between capacitance, area, distance and dielectric constant is $$ C=\frac{A E_{0}}{d} \Rightarrow C \propto \frac{1}{d} $$ Hence, if distance increases, capacitance decreases....

The distance of the field point on the equatorial plane of a small electric dipole is halved. By what factors will the electric field due to the dipole changes?

Ans: The formula $E x \frac{1}{r^{3}}$ gives the relation between electric field and distance. $$ \therefore E \propto \frac{1}{\left(\frac{r}{2}\right)^{3}} \Rightarrow E \propto \frac{8}{r^{3}} $$...

Force of attraction between two point electric charges placed at a distance d in a medium is $F$. What distance apart should these be kept in the same medium, so that force between them becomes $\frac{F}{3}$ ?

Ans: If two point charges are $q_{1}$ and $q_{2}$ separated by distance $d$, it can be expressed as: $\mathrm{F}=\frac{\mathrm{Kq}_{1} \mathrm{q}_{2}}{\mathrm{~d}^{2}}$ Suppose if force becomes...

What is the work done in moving a $2 \mu \mathrm{C}$ point change from corner $A$ to corner $B$ of a square $A B C D$ when a $10 \mu C$ charge exists at the centre of the square?

Ans: Point $A \& B$ are at the same distance from the point $O$. Hence,

Why does the electric field inside a dielectric decrease when it is placed in an external electric field?

Ans: The electric field that is present inside a dielectric decreases when it is placed in an external electric field because of polarisation as it creates an internal electric field which is...

Electric charge is uniformly distributed on the surface of a spherical balloon. Show how electric intensity and electric potential vary

a) on the surface Ans: Electric field intensity on the surface of the balloon would be, $$ E=\frac{\sigma}{\varepsilon_{0}} $$ Electric potential on the surface of the balloon would be, $$ V=\frac{K...

A sphere $S_{1}$ of radius $R_{1}$ encloses a charge $\mathbf{Q} .$ If there is another concentric sphere $S_{2}$ of radius $R_{2}\left(R_{2}>R_{1}\right)$ and there is no additional change between $S_{1}$ and $s_{2}$, then find the ratio of electric flux through $s_{1}$ and $s_{2}$. $\underline{S}_{2}$

Ans: We may recall that the expression for electric flux through a surface enclosing charge q by Gauss's law is given by, $$ \phi=\frac{q}{E_{0}} $$ Where, $\varepsilon_{0}$ is the permittivity of...

A sphere $S_{1}$ of radius $R_{1}$ encloses a charge $\mathbf{Q} .$ If there is another concentric sphere $S_{2}$ of radius $R_{2}\left(R_{2}>R_{1}\right)$ and there is no additional change between $S_{1}$ and $s_{2}$, then find the ratio of electric flux through $s_{1}$ and $s_{2}$. $\underline{S}_{2}$

Ans: We may recall that the expression for electric flux through a surface enclosing charge q by Gauss's law is given by, $$ \phi=\frac{q}{E_{0}} $$ Where, $\varepsilon_{0}$ is the permittivity of...

Two charges $+\mathrm{q}$ and $+9 \mathrm{q}$ are separated by a distance of $10 \mathrm{a}$. Find the point on the line joining the two charges where electric field is zero.

Ans: Let $p$ be the point (at $x$ distance from charge $+q$ ) on the line joining the given two charges where the electric field is zero. We know that the electric field at a point at r distance...

A particle of mass $m$ and charge a is released from rest in a uniform electric field of intensity E. Calculate the kinetic energy attained by this particle after moving a distance between the plates.

Ans: We have the electrostatic force on a charge a in electric field E given by. $\mathrm{F}=\mathrm{q} \mathrm{E} \quad \ldots \ldots(1)$ Also, we have Newton's second law of motion given by, $$...

If the net outward flux through the surface of the box were zero, could you conclude that there were no charges inside the box? Why or why not?

Ans: No. The net flux entering out through a body depends on the net charge contained in the body. If the net flux is given to be zero, then it can be inferred that the net charge inside the body is...

Careful measurement of the electric field at the surface of a black box indicate that the net outward flux through the surface of the box is $8.0 \times 10^{3} \mathrm{Nm}^{2} / \mathrm{C}$ a) What is the net charge inside the box?

Ans: It is given that: Net outward flux through surface of the box, $\phi=8.0 \times 10^{3} \mathrm{Nr}^{2} / \mathrm{C}$. For a body containing net charge a, flux is given by...

What is the net flux of the uniform electric field of exercise $1.15$ through a cube of side $20 \mathrm{~cm}$ oriented so that its faces are parallel to the coordinate planes?

Ans: It is given that all the faces of the cube are parallel to the coordinate planes. Clearly, the number of field lines entering the cube is equal to the number of field lines entering out of the...

When a glass rod is rubbed with a silk cloth, charges appear on both. A similar phenomenon is observed with many other pairs of bodies. Explain how this observation is consistent with the law of conservation of charge. Ans: Rubbing is a phenomenon in which there is production of charges equal in

Ans: Since unlike charges attract and like charges repel each other, the particles 1 and 2 moving towards the positively charged plate are negatively charged whereas the particle 3 that moves...

Why can one ignore the quantization of electric charge when dealing with macroscopic i.e., large scale charge?

Ans: When dealing with macroscopic or large-scale charges, the charges used are huge in number as compared to the magnitude of electric charge. Hence, the quantization of electric charge is of no...

An electric dipole when held at $30^{\circ}$ with respect to a uniform electric field of $10^{4} \mathrm{~N} / \mathrm{C}$ experiences a torque of $9 \times 10^{-26} \mathrm{Nm}$. Calculate dipole moment of the dipole?

Ans: It is given that $$ \begin{array}{l} \theta=30^{\circ} \\ \tau=9 \times 10^{-26} \mathrm{Nm} \\ E=10^{4} \mathrm{~N} / \mathrm{C} \end{array} $$ Dipole moment P needs to be calculated. It is...

The graph shows the variation of voltage $\mathrm{V}$ across the plates of two capacitors $\mathrm{A}$ and $\mathrm{B}$ versus increase of charge $\mathrm{Q}$ stored on them. Which of the two capacitors have higher capacitance? Give reason for your answer.

Ans: It is known that $c=\frac{Q}{V}$ Clearly, for a given charge $\mathrm{Q}$. $c \propto \frac{1}{V}$ Now, from the given graph, it is seen that $\mathrm{V}_{\mathrm{A}}

No two electric lines of force can intersect each other. Why?

Ans: Two electric lines of force can never intersect each other. Suppose if they intersect, then at the point of intersection, there can be two tangents drawn. These two tangents are supposed to...

A free proton and a free electron are placed in a uniform field. Which of the two experiences greater force and greater acceleration?

Ans: Force on both the electron as well as the proton in the uniform field would be equal because $\mathrm{F}=\mathrm{kq}$ and it is known that charge on both electron and proton are the same. On...

Define one coulomb.

Ans: Charge on a body is said to be 1 coulomb if it experiences a force of repulsion or attraction of $9 \times 10^{9} \mathrm{~N}$ from another equal charge when they are separated by a distance of...

Which physical quantity has its S.I. unit
1. $\mathrm{Cm}$ ?
2. $\mathrm{N} / \mathrm{C}$ ?

Ans: 1.The S.I. unit of electric dipole moment is $\mathrm{Cm}$. 2. The S.I. unit of electric field intensity is N/C.

A charged rod P attracts a rod R whereas P repels another charged rod Q. What type of force is developed between $Q$ and $R$ ?

Ans: Suppose that the rod $\mathrm{P}$ is negatively charged. As it attracts rod $\mathrm{R}$, it can be said that $\mathrm{R}$ is positively charged. Also, since $P$ repels rod $Q$, it can be said...

Does the force between two point charges change if the dielectric constant of the medium in which they are kept is increased?

Ans: Dielectric constant of a medium is given by $$ \begin{array}{l} k=\frac{F_{y}}{F_{M}}=\frac{\text { force between the charges in vaccum }}{\text { force between two charges in medium }} \\...

Unit of electric potential is i) joule/coulomb ii) joule-coulomb iii) volt/metre iv) joule/coulomb-metre.

Correct option is (i)

Distinguish between electric potential and electric potential energy.

Electric potential at a place in an electric field is the amount of effort done to bring the unit positive charge from infinity to that point, whereas electric potential energy is the energy...

The ratio of electric force between two electrons to two protons separated by the same distance in the air is: A $\quad 10^{\circ}$ B $\quad 10^{5}$ C $10^{\mathrm{t}}$ D None of these

Correct option is (A) $10^{\circ}$ $\frac{\mathrm{F}_{\mathrm{e}}}{\mathrm{F}_{\mathrm{p}}}=10^{0}=1$, because force depends only on charges, distance and nature of medium and not type of charge. As...

Two particles each of mass $\mathrm{m}$ and carrying charge $\mathrm{Q}$ are separated by some distance. If they are in equilibrium under mutual gravitational and electrostatic forces, then $Q / m$ (in $\mathrm{C} / \mathrm{Kg}$ ) is of the order of:
A $10^{-6}$
B $10^{-10}$
(C) $10^{-15}$
D $10^{-20}$

Correct option is (B) $10^{-10}$ Given : Gravitational force $=$ Electrostatics force Let the distance between the rwo charges be r. $$ \begin{array}{l} \Rightarrow \frac{\mathrm{G}(\mathrm{m})...

Electrostatic force and gravitational force differ in which respect?

In electrostatic force, the force of medium depends on charges while the force of the medium due to gravity does not depend on masses. There is no concept of induced mass.

Electrostatic force and gravitational force differ in which respect?
A Conservative force,
B Central force
c Principle of superposition
D Dependence on the intervening medium

Correct option is (D) Dependence on the intervening medium In electrostatic force, the force of the medium depends on charges while the force of the medium due to gravity does not depend on masses....

The excess (equal in number) number of electrons that must be placed on each of the two small spheres spaced 3cm apart with a force of repulsion between them to be $10^{-19} \mathrm{~N}$ is :
A 25
B 225
C 625
D 1250

Correct option is (C) 625 We need force of repulsion $=10^{-19} \mathrm{~N}$ Let $n$ no. of increase electrons be placed on each sphere $$ \begin{array}{l} \Rightarrow...

In comparison to the electrostatic force between two electrons, the electrostatic force between two protons is : A zero B smaller c same D greater

Correct option is(c) same Since the magnitude of the charge of electron and proton is the same, e, the electrostatic force between two protons is the same compared to the electrostatic force between...

In an A.C. circuit having resistance and capacitance :
A emf leads ahead of the current
B current lags behind the emf
c both the current and emf are in phase
D current leads ahead of the emf

Correct option is D current leads ahead of the emf $\mathrm{D}$ In circuits with primary capacitive loads, currently leads to the voltage. This is because the current must flow first to the two...

A parallel-plate air condenser of plate area A and separation d is charged to potential V and then the battery is removed. Now a slab of dielectric constant k is introduced between the plates. If Q, E, and W denote respectively the magnitude of the charge on each plate, the electric field between the plates (after the introduction of the dielectric slab) and work done on the system in the process of introducing the slab, then
A $\quad W=\frac{\xi_{10} \mathrm{~A} \mathrm{~V} \mathrm{~h}^{2}}{2 \mathrm{~d}}(1-1 / \mathrm{k})$
B $\quad Q=\frac{\xi_{1} K_{A} V}{d}$
c $\quad Q=\frac{\xi_{11} \mathrm{~A} \mathrm{~V}}{\mathrm{~d}}$
$\mathrm{D} \quad \mathrm{E}=\frac{\mathrm{V}}{\mathrm{kd}}$

Correct option is A $\mathrm{W}=\frac{\varepsilon_{0} \mathrm{~A} \mathrm{~V} \mathrm{~h}^{2}}{2 \mathrm{~d}}(1-1 / \mathrm{k})$ C $Q=\frac{\varepsilon_{0} A V}{d}$ D $\quad E=\frac{V}{k d}$ As...

A parallel plate capacitor with a dielectric slab of dielectric constant 3, filling the space between the plates, is charged to a potential V. The battery is then disconnected and the dielectric slab is withdrawn. It is then replaced by another dielectric slab of dielectric constant 2. If the energies stored in the capacitor before and after the dielectric slab is changed are $\mathrm{E}_{1}$ and $\mathrm{E}_{2}$, then $\mathrm{E}_{1} / \mathrm{E}_{2}$ is:
A $\frac{4}{9}$
B $\frac{2}{3}$
c $\frac{3}{2}$
D $\frac{9}{5}$

Correct option is B $\frac{2}{3}$ Let the charge stored by a capacitor with dielectric constant 3 be $Q$. Thus energy stored be $\frac{\mathrm{Q}^{2}}{2 \mathrm{C}_{1}}$ Since the charge remains the...

A parallel plate capacitor is first charged and then isolated, and a dielectric slab is introduced between the plates. The quantity that remains unchanged is:
A charge Q
B potential V
C capacity C
D energy U

The correct option is (A) charge Q When the capacitor is kept at a voltage, it gains charge. Now when the system is isolated, the charge present on the capacitor cannot change because of the law of...

When a dielectric slab is introduced between the two plates of the condenser then it’s capacity
A remains constant
B increases
C decreases
D may increase or decrease depending on the material of the dielectric slab

$\mathrm{~ O ~ W e i s c o d i s ~ T o p}$ Correct option is B increases As the dielectric slab is introduced there is some charge distribution in the slab and because of this, the electric field...

In the LCR circuit if resistance increases, then the quality factor
A) increases finitely
B decreases finitely
C remains constant
D None of these

The correct option is B decreases finitely Quality factor $Q$ is given by: $$ \mathrm{Q}=\frac{\omega_{0} \mathrm{~L}}{\mathrm{R}} $$ Thus, as $\mathrm{R}$ increases Q definitely decreases.

The magnitude of force between two plates of a capacitor is $|\mathrm{F}|=|\mathrm{Q}||\mathrm{E}|=$ Transformer works on.
A $\mathrm{AConly}$
B DC only
C Both $\mathrm{AC}$ and DC
D AC more effectively than DC

The correct option is A AC only Transformer works on the principle of Electromagnetic induction i.e an emf is induced in the coil if the magnetic flux linked with the coil changes. Magnetic flux in...

Force between two plates of a capacitor is :
A $\frac{\mathrm{Q}}{\varepsilon_{\|} \mathrm{A}}$
B $\frac{\mathrm{Q}^{2}}{2 \varepsilon_{11} \mathrm{~A}}$
C $\frac{\mathrm{Q}^{2}}{\mathrm{E}_{11} \mathrm{~A}}$
D none of these

Correct option is B $\frac{\mathrm{Q}^{2}}{2 \mathrm{\varepsilon}_{0} \mathrm{~A}}$ The magnitude of electric field by any one plate is $\mathrm{E}=\frac{\sigma}{2...

Quality factor of series resonance circuit is given by
A $\frac{\mathrm{f}_{2}-\mathrm{f}_{1}}{\mathrm{f}_{0}}$
B $\mathrm{f}_{2}-\mathrm{f}_{1}$
c) $\frac{\mathrm{f}_{1}-\mathrm{f}_{0}}{\mathrm{f}_{2}}$
D $\frac{\mathrm{f}_{0}}{\mathrm{f}_{2}-\mathrm{f}_{1}}$

Correct option is D $\frac{\mathrm{f}_{0}}{\mathrm{f}_{2}-\mathrm{f}_{1}}$ Quality factor is a relation between stored energy and energy dissipation in a device or system. As per definition of...

What is Q-factor? Write its expression and write the conditions for its maximum value.

Q-factor: In LCR Circuit, the ratio of resonance frequency to the difference of its neighboring frequencies so that their corresponding current is $1 / \sqrt{2}$ times of the peak value, is called...

Using Biot-Savart’s law, obtain an expression for the magnetic field at a distance r meter from an infinitely long wire carrying a current of i ampere.

Biot savart law is the base of all magnetism and the effects of current. It states that the magnetic field intensity due to an element of a current-carrying wire at a point near the element is...

The principle on which transformer works is?
A Mutual induction
B Self induction
C Electromagnetic induction
D None of these

The correct option is A Mutual induction Mutual inductance is where the magnetic field generated by a coil of wire induces a voltage in an adjacent coil of wire. A transformer is a device...

A transformer is
A) A device for stepping up D.C.
B )A generator of current
C) Device for converting direct current into alternating current
D) A device for stepping up or down the voltage of $A C$. supply

The correct option is D) A device for stepping up or down the voltage of $A C$. supply A transformer is a device that is used to either raise or lower voltages and currents in an electrical circuit....

Explain the construction of the transformer.

For the construction of the transformer, you must have two coils having mutual inductance and a laminated steel core. The two coils are insulated from each other and from the steel core. The device...

Write the principle and explain the construction and working of a transformer. Define its efficiency.

Principle: The transformer is based on the principle of electromagnetic induction. The phenomenon of producing an induced emf due to the changes in the magnetic flux associated with a closed circuit...

The phase difference between the applied emf and the line current in an anti-resonant circuit at resonance is
A $\frac{\pi}{2}$ radian
B $\pi$ radian
c $\frac{3 \pi}{2}$ radian
D zero

The correct option is D zero We know that phase difference is given by: $$ \phi=\arctan \left(\frac{\left(\mathrm{X}_{\mathrm{L}}-\mathrm{X}_{\mathrm{C}}\right)}{\mathrm{R}}\right) $$ at resonance...

The frequency at which the impedance of the circuit boorens mavimum is
a $\frac{1}{2 \pi} \sqrt{\frac{1}{L C}+\frac{R^{2}}{L^{2}}}$
b $\frac{1}{2 \pi} \frac{1}{\sqrt{1 C}}$
c $\frac{1}{2 \mathrm{z}} \sqrt{\frac{1}{\mathrm{LC}}-\frac{\mathrm{R}^{2}}{\mathrm{~L}^{2}}}$
D $\frac{1}{2 \mathrm{e}} \frac{\mathrm{R}}{\mathrm{L}}$

Correct option is c $\frac{1}{2 \pi} \sqrt{\frac{1}{L C}-\frac{R^{2}}{L^{2}}}$ Megritude of admittanos $Y=\frac{1}{Z}$ is given by: $$ |\mathrm{Y}|=\frac{\mid \mathrm{H}^{2}...

The resonent froquengy in an anti resonant circuitis:
a $\frac{1}{2 \mathrm{~s} \sqrt{L C}}$
b $\frac{1}{2 \mathrm{~s}} \sqrt{\frac{1}{\mathrm{LC}}-\frac{\mathrm{R}^{2}}{\mathrm{~L}^{2}}}$
c $\frac{1}{2 \mathrm{~s}} \sqrt{1 . \mathrm{C}}$
D $\frac{1}{2 \pi} \sqrt{\frac{C}{L}}$

Correct option is a $\frac{1}{2 \pi \sqrt{L C}}$ For rescnance $$ \mathrm{X}_{\mathrm{L}}=\mathrm{X}_{\mathrm{E}} $$ $$ \begin{aligned} \mathrm{kL} &=\frac{1}{\mathrm{wC}} \\ \mathrm{w}...

The study of the earth’s magnetic field is called
A Terrestrial Magnetism
B Magneto Therapy
C Special Magnetism
D None of these

The correct option is A Terrestrial Magnetism

Power consumed in an AC circuit becomes zero if
A Inductance and resistance are both high.
B inductance and resistance are both low.
C inductance is very high and resistance is negligible.
D inductance is low and resistance is high.

The correct option is C inductance is very high and resistance is negligible. The power consumption in an AC circuit is zero when the circuit contains only inductance or capacitance since the...

The terminal potential difference of a cell is equal to the emf of the cell when:

The terminal potential difference of a cell is equal to the emf of the cell when: → The cell is an open circuit. → The internal resistance of the cell is zero. → The load resistance much greater...

What do you understand by angle of dip?

The angle of dip is the angle between the direction of the earth's magnetic field and the plane of the horizon

State true and false, mass is not conserved during a chemical reaction.
True
False

The correct option is False In a chemical reaction, the total mass of the reactants is equal to the total mass of the product hence the mass remains conserved in a chemical reaction.

A circular coil a carrying current produces a magnetic field $\mathrm{B}_{0}$ at its centre. This coil is made itself to 10 turns and the same current is set up in it. The magnetic field $\mathrm{B}$ at its centre would be
A $\quad \mathrm{B}=\mathrm{B}_{0}$
B $\quad \mathrm{B}=10 \mathrm{~B}_{0}$
C $\quad \mathrm{B}=50 \mathrm{~B}_{0}$
D $\quad B=100 B_{0}$

Correct option is B $\mathrm{B}=10 \mathrm{~B}_{0}$ Electric current in a circular loop creates a magnetic field which is more concentrated in the center of the loop than outside the loop....

An electric current i is flowing in a circular coil of radius a. At what distance from the center of the axis of the coil will the magnetic field be $\frac{1}{8}$ of its value at the centre?
A $3 \mathrm{a}$
в $\sqrt{3} a$
c $\frac{\mathrm{a}}{3}$
D $\frac{\mathrm{a}}{\sqrt{3}}$

Correct option is B $\sqrt{3} \mathrm{a}$ Magnetic field due to the circular current (I) carrying coil of radius $\mathrm{a}$, at a distance $r$ from the center of the coil is given by: $$...

(a) Determine the value of phase difference between the current and the voltage in the given series LCR circuit. (b) Calculate the value of the additional capacitor which may be joined suitably to the capacitor C that would make the power factor of the circuit unity

(a)The phase difference between current and voltage $\phi$ is given by $$ \begin{array}{l} \tan \phi=\frac{\mathrm{X}_{\mathrm{C}}-\mathrm{X}_{\mathrm{L}}}{\mathrm{R}} \\...

An ammeter of resistance $0.2 \Omega$ and range $10 \mathrm{~mA}$ is to be used to read potential difference upto 1 volt. It will have to be connected to A $99.8 \Omega$ resistance in series B $99.8 \Omega$ resistance in parallel C $0.1 \Omega$ resistance in parallel D $0.1 \Omega$ resistance in series

Correct option is A $99.8 \Omega$ resistance in series $$ \begin{array}{l} \mathrm{V}=\mathrm{I}_{g}\left(\mathrm{R}+\mathrm{R}_{g}\right) \\ \therefore 1=10 \times 10^{-3} \times(\mathrm{R}+0.2) \\...

A circular current carrying coil has a radius r. Find the distance from the centre of coil, on its axis, where the magnetic induction will be 1/8 th of its value at the centre of coil.

$$ \begin{array}{l} B_{A}=\frac{\mu_{1} I}{2} \times \frac{r^{2}}{\left(x^{2}+r^{2}\right) \frac{3}{2}}\\ \mathrm{B}_{0}=\frac{\mu_{1} \mathrm{I}}{2} \times \frac{\mathrm{r}^{2}}{\mathrm{r}^{3}}\\...

Explain the term ‘drift velocity’ of electrons in a conductor. Hence obtain the expression for the current through a conductor in terms of ‘drift velocity’.

The average velocity of all the free electrons in the conductor is called the drift velocity of free electrons of the conductor. When a conductor is connected to a source of emf an electric field is...

Given below are some fomous numbers associated with electromagnetic radiation in different contexts in physics .State the part of the electromagnetic spectrum to which each belongs . 21 cm (wavelength emitted by atomic hydrogen in interstellar space ).

Radiation of wavelength of 21 cm : It corresponding to radio waves of short wavelength.

The resistance required to be connected in parallel to an ammeter in order to increase its range 10 times, will be
A one-tenth the resistance of ammeter
B nine times the resistance of ammeter

C ten times the resistance of ammeter
D one-ninth the resistance of ammeter

Correct option is D one-ninth the resistance of ammeter Full scale deflection voltage be V Now initiall range is I $$ \mathrm{V}=\mathrm{IR} $$ Now, Range is made $10 \mathrm{I}$ $$ \begin{array}{l}...

Which part of the electromagnetic spectrum is used in operating a RADAR?

Microwaves are used in operating a RADAR.

Which part of electromagnetic spectrum does the wavelength $10^{-10} \mathrm{~m}$ correspond to?

$\mathrm{X}$-rays part of electromagnetic spectrum does the wavelength $10^{-10} \mathrm{~m}$ correspond to.

In the order of increasing frequency, the electromagnetic spectrum may be arranged as
A Gamma rays, $\mathrm{X}$-rays, visible light, radio waves
B $\mathrm{X}$-rays $_{7}$ gamma rays, visible light, radio waves
C Radio waves, visible light, $\mathrm{X}$-rays, gamma rays
D Radio waves, visible light, gamma rays, $\mathrm{X}$-rays

Correct option is C Radio waves, visible light, $\mathrm{X}$-rays, gamma rays The electromagnetic spectrum is a continuum of all electromagnetic waves arranged according to frequency and wavelength....

Find the expression of magnetic, field produced at the centre of current carrying circular coil.

Consider a circular coil of radius a and carrying current I in the direction shown in Figure. Suppose the loop lies in the plane of paper. It is desired to find the magnetic field at the centre...

The magnetic field in a plane electromagnetic wave is given by $$ B=(200 \mu T) \sin \left[\left(4.0 \times 10^{1} 5_{s}{ }^{-1}\right)(t-x / c)\right] $$ Find the maximum electric field and the average energy density corresponding to the electric field.

Given: The magnetic field in a plane electromagnetic wave is given by $$ \mathrm{B}=(200 \mu \mathrm{T}) \sin \left[\left(4.0 \times 10^{1} 5_{\mathrm{s}}^{-1}\right)(\mathrm{t}-\mathrm{x} /...

Two charges $5 \times 10^{-8} \mathrm{C}$ and $-3 \times 10^{-8} \mathrm{C}$ are located $16 \mathrm{~cm}$ apart. At what point $(\mathrm{s})$ on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.

Let $\mathrm{p}$ be the point of zero potential be $\mathrm{p}$ at distance $\mathrm{r}$ from the charge $1 .$ $\mathrm{d}=16 \mathrm{~cm}$ Electric potential, $\mathrm{v}=\mathrm{q}_{1} / 4 \pi...

An electric dipole has the magnitude of its charge as q and its dipole moment is p. It is placed in uniform electric field E. If its dipole moment is along the direction of the field, the force on it and its potential energy are respectively
A q.E and max
B $\quad 2 q . E$ and $\min$.
C q.E and $\min$
D zero and min.

Correct option is D zero and min. When the dipole is in the direction of field then net force is $\mathrm{q} \mathrm{E}+(-\mathrm{q} \mathrm{E})=0$ and its potential energy is minimum $=-$ p.E...

What is the angle between the electric dipole moment and the electric field due to it on the axial line?
A $0^{\circ}$
VB $90^{\circ}$
C $180^{\circ}$
D none of these

Correct option is A $0^{\circ}$ Electric field $\overrightarrow{\mathrm{E}}$ is along the dipole axis $\therefore \theta=0^{\circ}$

Why do magnetic field lines not intersect each other?

If magnetic field lines cross, there will be two directions of the same field at the crossing point, which is not conceivable. As a result, the field lines do not cross or intersect

Explain the working of P-N junction diode in forward and reverse biased mode

When the positive terminal of a cell or battery is connected to the p-side of the junction and the negative terminal to the n side, the diode is said to be forward biassed. The depletion region...

State Bohr’s Model.

The Bohr Atomic Model's Postulates Electrons orbit the nucleus in a predetermined circular path known as "orbits," "shells," or "energy levels." Each circular orbit has a given quantity of energy,...

1) The Bohr atomic model hypothesis made correct predictions for lower sized atoms like hydrogen, but poor spectrum predictions were achieved when larger atoms were taken into account. 2) When the spectral line is split into numerous components in the presence of a magnetic field, it fails to explain the Zeeman phenomenon.

1) The Bohr atomic model hypothesis made correct predictions for lower sized atoms like hydrogen, but poor spectrum predictions were achieved when larger atoms were taken into account. 2) When the...

What is displacement current?

Current passes through the circuit while a capacitor is charging (or draining). However, no actual charge transfer occurs in the insulated region between the capacitors, which is incompatible with...

List the properties of electromagnetic waves

The oscillating electric and magnetic fields at right angles to one other make up electromagnetic waves. Properties Electric fields and magnetic fields oscillate at right angles to one other to...

What is displacement current? Obtain an expression of displacement current for a charged capacitor. Write Ampere-Maxwell’s law.

Current passes through the circuit while a capacitor is charging (or draining). However, no actual charge transfer occurs in the insulated region between the capacitors, which is incompatible with...

The electromagnetic waves travel in free space with the velocity of
A Sound
B Light
c Greater than that of light
D Greater than that of sound

Correct option is B Light Electromagnetic waves travel in free space or vacuum with the velocity of light, $\mathrm{c}=3 \times 10^{8} \mathrm{~m} / \mathrm{s}$

What is the wavelength of the wave whose frequency is $10^{12} \mathrm{~Hz}$ ?
A $\quad 0.3$
B $0.4$
C $0.5$,
D $0.6$

Correct option is A $0.3$ $$ \mathrm{C}=\mathrm{v} \lambda $$ $$ \lambda=\frac{\mathrm{c}}{\mathrm{v}}=\frac{3 \times 10^{8}}{10^{12}} $$ $$ \begin{array}{l} =3 \times 10^{-4} \mathrm{~m} \\ =0.3...

If the instantaneous magnetic flux and induced emf produced in a coil is $\phi$ and $\mathrm{E}$ respectively, then according to Faraday’s law of electro magnetic induction:
A $\quad$ E must be zero if $\phi=0$ and changing
B $\quad E \neq 0$ if $\phi=0$
C $E \neq 0$ if $\phi$ is changing.
D $E=0$ then $\phi$ must be zero

Correct option is c $E \neq 0$ if $\phi$ is changing. Farady's law states that time varying magnetic flux can induce an e.m.f. $\mathrm{E}=$ Electric field, Induced $$ \mathrm{E}=-\frac{\mathrm{d}...

How electromagnetic waves are produced

Moving charges produce electromagnetic waves, which are a mix of electric and magnetic field waves. A charged particle is the starting point for all electromagnetic waves. An electric field is...

Write Faraday’s laws of electro magnetic induction.

There are two Faraday's laws of Electromagnetic induction, 1) First Law: Whenever magnetic flux linked with the circuit changes, an emf is induced in it. 2)Second Law: The magnitude of emf is...

If the instantaneous magnetic flux and induced emf produced in a coil is $\phi$ and $E$ respectively, then according to Faraday’s law of electro magnetic induction:
A E must be zero if $\phi=0$ and changing
B $\quad E \neq 0$ if $\phi=0$
c $E \neq 0$ if $\phi$ is changing.
D $E=0$ then $\phi$ must be zero

Correct option is c $E \neq 0$ if $\phi$ is changing. Farady's law states that time varying magnetic flux can induce an e.m.f. $\mathrm{E}=$ Electric field, Induced $$ \mathrm{E}=-\frac{\mathrm{d}...

The induced emf produced when a magnet is inserted into a coil does not depend upon:
A The number of turns in the coil
B The resistance of the coil
C The speed of approach of the magnet
D All the above

Correct option is B The resistance of the coil The induced emf produced when a magnet is inserted into a coil does not depend upon the resistance of the coil.

When current changes from $4 \mathrm{~A}$ to $0 \mathrm{~A}$ in $0.1 \mathrm{~s}$ in an inductor the induced emf is found to be $100 \mathrm{~V}$, then find the value of self-inductance is :
A $0.5 \mathrm{H}$
B $2 \mathrm{H}$
C $2.5 \mathrm{H}$
D $1 \mathrm{H}$

Correct option is C $2.5 \mathrm{H}$ $$ \begin{array}{l} \Delta \mathrm{I}=(4-0)=4 \mathrm{~A} \\ \mathrm{t}=0.1 \mathrm{~s} \\ \mathrm{e}=100 \mathrm{~V} \\...

State whether true or false : Soft iron is used in electromagnets because soft iron does not retain magnetism permanently.
A True
B False

Correct option is A True Soft iron core is used in electromagnets because soft iron does not retain magnetism permanently, that is, it loses the magnetism as soon as magnetic field is removed. Hence...

The unit of inductance is
A Volt /Ampere
B Joule/ampere
C Volt-sec/ampere
D Volt-ampere $/ \mathrm{sec}$

Correct option is (C) Volt-sec/ampere $$ \begin{aligned} e &=L \frac{d i}{d t} \\ \Rightarrow & L=\frac{V \text { olt }-\text { sec }}{\text { Ampere }} \end{aligned} $$

Consider the following statements :
(i) Soft iron conducts electricity
(ii) Soft iron is magnetic material
(iii) Soft iron is used for magnetic permanent magnets
(iv) Soft iron is used as electro magnet
A (i) and (ii) are correct
B (i) and (iii) are correct
C (ii) and (iv) are correct
D (i), (ii) and (iv) are correct

Correct option is D (i), (ii) and (iv) are correct Soft iron conducts electricity It is a magnetic material It is not used for magnetic permanent magnets It is used as electro magnet

Alnico is used for making permanent magnets because it has
A High coercivity and high retentivity
B high coercivity and low retentivity
C low coercivity and low retentivity
D low coercivity and high retentivity

The correct option is A High coercivity and high retentivity Since of its high coercivity and low retentivity, Alnico is used to make permanent magnets because it can be quickly magnetised in an...

For making an electro-magnet, substance should be of
i) high retentivity and high coercivity
ii) low retentivity and high cocrcivity
iii) high retentivity and low coercivity
iv) low retentivity and low coercivity

CORRECT OPTION IS iii) high retentivity and low coercivity The capacity of a substance to remain magnetised after the external magnetising field has vanished is known as retentivity. A material with...

Electrical resistivity of a given metallic wire depends upon:
A its length
B its thickness
C its shape
D nature of the material

Correct option is D nature of the material Hint: Resistivity is an intrinsic property of a metal. Step 1: Explanation of Resistivity Resistivity of a metallic wire does not depend on its geometry...

The resistivity of a wire depends on its
A length
B area of cross-section
c material
D all of the above three factors

Correct option is (C) material The resistivity or specific resistance of a material is an intensive property (property which does not depend on the system size or the amount of material in the...

What are the factors on which resistance of a conductor depends

Resistance can be defined as $$ \begin{array}{l} \mathrm{R} \propto \frac{1}{\mathrm{~A}} \\ \Rightarrow \mathrm{R}=\rho \frac{1}{\mathrm{~A}} \end{array} $$ where $\rho=$ specific resistance or...

The product of resistivity and specific conductivity of a cylindrical conductor depends on
i) temperature
ii) material
iii) area of cross-section
iv) none of these

Correct option is (iv) None of the above The product of resistivity and conductivity of a cylindrical conductor is constant The product becomes $\rho \times \sigma$, where pis resistivity and...

An infinite plane sheet of charge in vacuum has a uniform surface charge density $\sigma$. The electric field intensity near it is
A $\frac{\sigma}{\varepsilon_{0}}$
B $\frac{\sigma}{2 \varepsilon_{0}}$
C $\frac{\sigma}{\varepsilon}$
D $\frac{\sigma}{2 \varepsilon}$

Correct option is A $\frac{\sigma}{\varepsilon_{0}}$ Charge density $=\sigma$ Electric field intensity near it is - Using gauss law, $\lambda=\frac{\sigma}{\varepsilon_{0}}$

Which of the following is not a unit of electric field intensity?
A $\frac{\mathrm{V}}{\mathrm{m}}$
B $\frac{N}{C}$
c $\frac{\text { dyne }}{\text { statcoulomb }}$
D None of these

Correct option is D None of these $$ \begin{array}{l} \mathrm{F}=\mathrm{q} \mathrm{E} \\ \mathrm{E}=\frac{\mathrm{F}}{\mathrm{q}}=\frac{\mathrm{N}}{\text { Coulomb }}=\mathrm{NC}^{-1}=\text { SI...

A current i ampere flows along an infinitely long straight thin walled tube, then the magnetic induction at any point inside the tube is
A infinite
B zero
C $\frac{\mu_{0}}{4 \pi} \cdot \frac{2 i}{T}$ tesla
D $\frac{2 \mathrm{i}}{\mathrm{r}}$ tesla

Correct option is B zero Using ampers law, there is no current enclosed in the pipe $\int \overline{\mathrm{B}} \cdot \overline{\mathrm{dl}}=\mu_{0}$ Ienclosed

A current i amp flows along an infinitely long straight thin conductor. Then the magnetic induction at any point on the axis of the conductor is
A infinity
B zero
C $\frac{\mu_{n} 2 i}{4 \pi r}$
D $\frac{\mu_{0}}{4 \pi^{\frac{i}{\mathrm{~T}}}}$

Correct option is B zero $\operatorname{Sin} \theta=0$ on any pt, on the axis of conductor carrying current $$ \mathrm{B}=\frac{\mu_{0}}{4 \Pi} \mathrm{i} \frac{\mathrm{d}] \operatorname{Sin}...

Two thin, long, parallel wires, separated by a distance ‘ $\mathrm{d}$ ‘ carry a current of ‘ $\mathrm{i}$ ‘ $\mathrm{A}$ in the same direction. They will
A repel each other with a force of $y_{0} \mathrm{i}^{2} /(2 \pi \mathrm{d})$
B attract each other with a force of $\mu_{n} \mathrm{i}^{2} /(2 \pi \mathrm{d})$
C repel each other with a force of $y_{0} i^{2} /\left(2 \pi \mathrm{rd}^{2}\right)$
D attract each other with a force of $\mu_{\mu_{1}} 1^{2} /\left(2 \pi \mathrm{d}^{2}\right)$

Correct option is B attract each other with a force of $y_{0} i^{2} /(2 \pi \mathrm{d})$ $$ \frac{\mathrm{F}}{\mathrm{l}}=\frac{\mu_{0} \mathrm{i}_{1} \mathrm{i}_{2}}{2 \pi \mathrm{d}} $$ $$...

Two very long straight parallel wires carry steady currents i and $2 \mathrm{i}$ in opposite directions. The distance between the wires is $\mathrm{d}$. at a certain instant of time, a point charge $\mathrm{q}$ is at a point equidistant from the two wires in the plane of the wires. Its instantaneous velocity $\vec{v}$ is perpendicular to this plane. The magnitude of the force, due to the magnetic field acting on the charge at this instant is:
A $\frac{\mu_{n} i q v}{2 \pi d}$
B $\frac{\mu_{n} \text { iqv }}{\pi d}$
C $\frac{3 \mu_{n} \mathrm{iqv}}{2 \pi \mathrm{d}}$
D zero

Correct option is (D) zero Magnetic field at P is perpendicu;ar to paper inward due to both the wires. Charged particle is also projected in the same direction. So, force on the charged particle is...

A charge $\mathrm{q}$ is moving with a velocity v parallel to a magnetic field $\mathrm{B}$. Force on the charge due to magnetic field is
A quB
B $\quad q \quad B / v$
C zero
D $\mathrm{Bv} / \mathrm{q}$

Correct option is C zero $$ \begin{array}{l} \mathrm{F}_{\mathrm{n}}=\mathrm{q}(\overrightarrow{\mathrm{v}} \times \overrightarrow{\mathrm{B}}) \\ =\mathrm{qvB} \sin \theta \\ =0 \text { (because }...

The force $F$ acting on charge $q$ moving with velocity $v$ perpendicular to magnetic field $B$ is
i) $\quad F=q v B$
ii) $\quad F=\frac{q v}{B}$
iii) $\quad F=\frac{q B}{v}$
iv) $\quad F=\frac{B v}{q}$

Correct option is (I) $F=q v B$ Magnetic force $\mathrm{F}=\mathrm{q}(\mathrm{v} \times \mathrm{B})=\mathrm{qvB} \sin \theta$ where $\theta$ is the angle between $v$ and $B$. Given:...

The length of a metallic wire of $50 \Omega$ resistance is stretched two times its initial length. Its new resistance is
i) $25 \Omega$
ii) $50 \Omega$
iii) $100 \Omega$
iv) $200 \Omega$

Correct option is (iv) $200 \Omega$ Resistance of wire $\mathrm{R}=\rho \frac{\mathrm{L}}{\mathrm{A}}=\rho \frac{\mathrm{L}^{2}}{\mathrm{AL}}=\rho \frac{\mathrm{L}^{2}}{\mathrm{~V}}$...

The unit of electric field intensity is
i) newton/metre
ii) coulomb/newton
iii) newton/coulomb
iv) joule/newton

iii) newton/coulomb The amount of force experienced by a unit charged particle when it is placed in the electric field is known as Electric field intensity. The S.I unit of electric field intensity...

A Carnot engine, having an efficiency of $\eta=\frac{1}{10}$ as heat engine, is used as a. refrigerator. If the work done on the system is $10 \mathrm{~J}$, the amount of energy absorbed from the reservoir at lower temperature is:
A $90 \mathrm{~J}$
B $1 \mathrm{~J}$
c $100 \mathrm{~J}$
D $99 \mathrm{~J}$

Correct option is A $90 \mathrm{~J}$ efficiency of carnot cycle is given as $$ \eta=\frac{W}{Q_{H}} $$ where $W$ is work done and $Q_{H}$ is amount of heat added to system. $$ \begin{array}{l}...

Two identical sonometer wires have a fundamental frequency of $500 \mathrm{~Hz}$, when kept under the same tension. What fractional increase in the tension of one wire would cause an occurrence of 5 beats $/ \mathrm{sec}$, when both wires vibrate together?
A 2
B 3
C 4
D 5

Solution (A) 2 $\mathrm{n} \propto \mathrm{V}$ and $\mathrm{V} \propto \sqrt{T}$ $$ \Rightarrow \mathrm{n} \propto \sqrt{\mathrm{T}} . .(1) $$ 5 beats/sec are obtained when the frequency of one...

The amplitude, frequency and velocity of the component waves producing a stationary wave are $8 \mathrm{~cm}, 30 \mathrm{~Hz}$ and $180 \mathrm{~cm} /$ second respectively. Write the equation of stationary wave

Since the waVe equation of a travelling wave:- $y=a \sin 2 \pi(t / T-x / \pi)$ $\mathrm{a}=$ Amplitude $t=$ time $\mathrm{T}=$ Time Period $x=$ Path difference $\pi=$ wavelength Let...

The equation of simple harmonic wave is given by $y=6 \sin 2 \pi(2 t-0.1 x)$, where $x$ and $y$ are in $m m$ and $t$ is in seconds . The phase difference between two particles $2 \mathrm{~mm}$ apart at any instant is
A $18^{0}$
B $36^{\circ}$
C $54^{0}$
D $72^{0}$

Correct option is D $72^{\circ}$ Given equation can be written as $y=6 \sin (4 \pi t-0.2 \pi x)$ $\therefore$ Phase $\phi=-0.2 \pi x$ $\Rightarrow \phi_{1}=-0.2 \pi \mathrm{x}_{1}$ and...

Derive expression for the ratio of specific heats $\gamma$ if the gas has $\mathrm{f}$ degrees of freedom.

$\mathrm{~ O ~ W e i r i s o s t y ~ T o p p r}$ The molar specific heats of a gas having $\mathrm{f}$ degrees of freedom is given by : $$ \mathrm{C}_{\mathrm{r}}=\frac{1}{2} \mathrm{f} \mathrm{R}...

At what temperature the average translational $\mathrm{KE}$ of the molecules of a gas will become equal to the $\mathrm{KE}$ of an electron accelerated from rest through $1 \mathrm{~V}$ potential difference?
A $\quad 10^{6} \mathrm{~K}$
B $2.34 \times 10^{4} \mathrm{~K}$
c $7.73 \times 10^{3} \mathrm{~K}$
D none of these

Correct option is C $7.73 \times 10^{3} \mathrm{~K}$ $$ \frac{3}{2} \mathrm{KT}=1 \mathrm{eV}=1.6 \times 10^{-19} \mathrm{~J} $$ Or" $$ \mathrm{T}=\frac{2 \times 1.6 \times 10^{-19}}{3 \times 1.38...

What is surface energy? Establish the relation between surface tension and surface energy

$S=$ surface tension of soap Liquid $1=$ length of $\mathrm{PQ}$ Total Inward Force on the wire P Q $$ F=S \times 21 $$ To increase surface area we have to pull wire $\mathrm{P} \mathrm{Q}$ outwards...

The elastic energy stored per unit volume in a stretched wire is
A $\frac{1}{2} \frac{\text { (stress) }}{\mathrm{Y}}$
B $\frac{1}{2} \frac{(\text { stress })^{2}}{\mathrm{Y}}$ ,br>C $\frac{1}{2} \frac{(\text { stress })^{2}}{\mathrm{Y}^{2}}$
D $\frac{1}{2} \frac{\text { (stress) }}{\mathrm{Y}^{2}}$

Correct option is B $\frac{1(\text { stress })^{2}}{2}$ The elastic energy stored per unit volume in a stretched wire is $$ \mathrm{u}=\frac{1}{2} \times \text { stress } \times...

. The linear density of a vibrating string is $1.3 \times 10^{-4} \mathrm{~kg} / \mathrm{m} . \mathrm{A}$ transverse wave is propagating on the string and is described by the equation $\mathrm{Y}=0.021 \sin (\mathrm{x}+3 \circ \mathrm{t})$ where $\mathrm{x}$ and $\mathrm{y}$ are measured in meter and t in second. Ten sion in the string is
A $\quad 0.12 \mathrm{~N}$
B $\quad 0.48 \mathrm{~N}$
C $1.20 \mathrm{~N}$
D $4.8 \mathrm{oN}$

Correct option is A $0.12 \mathrm{~N}$ Linear density $\mu=1.3 \times 10^{4} \mathrm{Kg} / \mathrm{m}$ Wave equation $y=0.021 \sin (x+30 t)$ Velocity of wave...

5 mole of oxygen are heated at constant volume from $10^{\circ} \mathrm{C}$ to $20^{\circ} \mathrm{C} .$ What will be the change in the internal energy of gas? The molar heat of oxygen at constant pressure, $\mathrm{C}_{\mathrm{p}}=7.03 \mathrm{cal} \mathrm{mol}^{-1} \mathrm{deg}^{-1}$ and $\mathrm{R}=8.31 \mathrm{~J} \quad$ mol $^{-1} \mathrm{deg}^{-1}$

$\mathrm{R}=8.31 \mathrm{~J} \quad \mathrm{~mol}^{-1} \mathrm{deg}^{-1}=\frac{8.31}{4.18} \mathrm{cal} \mathrm{mol}^{-1} \mathrm{deg}^{-1}$ $=1.99 \mathrm{cal} \mathrm{mol}^{-1} \mathrm{deg}^{-1}$...

State and explain the law of conservation of angular momentum. Give two examples to illustrare the law

Law of conservation of angular momentum states that in the absence of an external torque, the total angular momentum is conserved or the total angular momentum of an isolated system remains constant...

Write the law of conservation of angular momentum. Write two examples based on this

When there is no net torque applied to a system, such as a rotating item or objects, the law of conservation of angular momentum asserts that angular momentum is conserved. An ice skater performing...

The surface area of a black body is $5 \times 10^{-4} \mathrm{~m}^{2}$ and temperature is $727^{\circ} \mathrm{C}$. How much heat is radiated per minute by it

Stefan's constant = $5 \cdot 67 \times 10^{-8}$ joule $/\left(\mathrm{m}^{2}-\sec -\mathrm{K}^{4}\right)$ The power radiated is given by Stefan's law: $$ \mathrm{P}=\sigma \mathrm{AeT}^{4} $$...

The angular acceleration of particle moving along a circular path with uniform speed
A uniform but non zero
B zero
C variable
D such as can not be predicted from given information

The correct option is B zero The velocity of the particle is constant i.e $\mathrm{v}=$ constant Using $\mathrm{v}=\mathrm{rw} \quad \Longrightarrow \mathrm{w}=$ constant $\therefore$ Angular...

What do you mean by centripetal acceleration ? Deduce the formula for centripetal acceleration of a body executing circular motion with uniform velocity in terms of angular velocity

rate of change of tangential velocity is called as the centripetal acceleration. $$ \mathrm{F}=\frac{\mathrm{mv}^{2}}{\mathrm{r}} $$ centripetal acceleration is given by, $$...

Write Bernoulli’s theorem

Bernoulli's principle asserts that the entire mechanical energy of a moving fluid, which includes gravitational potential energy of elevation, fluid pressure energy, and fluid motion kinetic energy,...

What is Hooke’s law ?

In the year 1660, an English scientist named Robert Hooke discovered Hooke's law, commonly known as the law of elasticity. "When an object has a relatively minor deformation, the magnitude of the...

Write down the theorem of perpendicular axes of moment of inertia

The perpendicular axis theorem asserts that the moment of inertia of a planar lamina (i.e. 2-D body) at an axis perpendicular to the plane of the lamina is equal to the sum of the moments of inertia...

The earth revolves around the sun in a circular path with a speed of $30 \mathrm{~km} / \mathrm{s}$. What is the radial acceleration directed towards the sun?

$$ \begin{array}{c} \text { Speed of revolution }=30 \mathrm{Km} / \mathrm{s} \\ =3 \times 10^{4} \mathrm{~m} / \mathrm{s} \end{array} $$ Time of revolution $=$ One year $=356$ days (convert into...

A wave represented by an equation $y=a \cos (k x-\omega t) \quad$ superimposes with another wave and produces stationary wave. At $x=0$ node is formed. The equation of the second wave is
i) $y=a \sin (k x+\omega t)$
ii) $y=-a \cos (k x-\omega t)$
iii) $y=-a \sin (k x-\omega t)$
iv) $y=-a \cos (k x+\omega t)$

Correct option is D $-\mathrm{a} \cos (\mathrm{kx}+\omega \mathrm{t})$ To form a stationary wave with $y=a \cos (k x-w t)$ the wave should be in the opposite direction of this wave and amplitude...

How is the rise of liquid affected if the top of the capillary is closed?

If the top of the capillary tube is closed, there will be a little rise in the capillary tube. Because the downward force exerted by compressed air above the liquid in the tube opposes the rise of...

The liquid rises in capillary tube when the angle of contact is
i) obtuse angle
ii) acute angle
iii) $\frac{\pi}{2}$ radian
iv) $\pi$ radian.

Correct option is ii) acute angle Liquid rises in a capillary tube if the angle of contact is acute, but liquid falls in a capillary tube if the angle of contact is obtuse

Write chromyl chloride test with equation

Chloride radical is detected by the chromyl chloride test. In this test, chromyl chloride gas (orange red color) is produced. Equation Involved – 4NaCl + K2Cr2O7 + 6H2SO4 → 4NaHSO4 + 2KHSO4 + 3H2O +...

What do you understand by lanthanide contraction

The lanthanide contraction is the decrease in the atomic or ionic radii with increase in the atomic number of lanthanides

What are lanthanide elements?

Lanthanide elements resembles a lot in properties with lanthanum. Lanthanide is group of 14 elements from atomic number 58 to 71. In these elements on increasing atomic number electron enters into...

Explain oxidization properties of potassium permanganate in acidic medium.

2KMnO4 + 8H2SO4 + 10KI → 6K2SO4 + 8H2O + 5I2 2KMnO4 + 5SO2 + 2H2O → 2MnSO4 + 2H2SO4 + K2SO4 2KmO4 + 16HCl → 2KCl + 2MnCl2 + 8H2O + 5Cl2 5COOH – COOH + [5O] → 10CO2 + 5H2O

Why depletion of ozone layer threat to us ?

The ozone layer's depletion has negative consequences for the environment. Let's look at the key consequences of ozone depletion on humans and the environment. Human Health Effects Due to the ozone...

Draw a labelled diagram of female reproductive system ?

How are water and minerals transported in plants?

The Xylem transports water and minerals in plants. - Root hairs are hairs that grow on a plant's roots. Because they are in close touch with the water layer between the soil particles, these root...

What are the functions of digestive enzymes ?

Enzymes are proteins with specific functions. They're found in all living cells and are required for every chemical reaction that takes place in the body. Each enzyme is responsible for a specific...

Mention two differences between ‘Artery’ and ‘Vein’.

One of the fundamental differences between arteries and veins is that arteries deliver oxygenated blood to all body areas, whereas veins, with the exception of pulmonary arteries and veins, carry...

What happens when metals react with water?

When a metal reacts with water, a metal hydroxide is generated, as well as hydrogen gas. The chemical reactivity of a metal determines the degree of its interaction with water. Some metals respond...

write the valency of magnesium ?

The valency of magnesium is 2.

Write balanced chemical equations for the reation taking place when – (A) Dilute Sulphuric acid reacts with Zinc

H2SO4(aq)+Zn(s)→ZnSO4(aq)+H2(g)

What do you mean by a precipitation reaction?

In our daily lives, we see a lot of chemical reactions. Burning, corrosion, food heating, and digestion are all instances of such interactions. Precipitation reactions are a common type of chemical...

What is electric power? Derive $\mathrm{H}=\mathrm{I}^{2} \mathrm{Rt}$, where $\mathrm{H}$ is the amount of heat produced by steady curnent I through a resistor $\mathbf{R}$ in time t.

Electric power is the rate at which electrical energy is transferred by an electric circuit per unit of time. The watt, or one joule per second, is the SI unit of power. Electric generators are the...

Draw a labelled diagram of an electric motor. Explain its principle and working. What is the function of split ring in an electric motor?

In an electric motor, electrical energy is turned into mechanical energy. Electric motor operation: When a current is fed through the coil PQRS, the coil begins to rotate anticlockwise because a...

Why two magnetic lines of force do not intersect each other?

The intensity of the magnetic lines is constant throughout and proportional to their proximity. Reason - The two magnetic field lines do not connect because if they did, the compass needle would...

Why are we looking at alternate sources of energy?

They are long-term. The renewable energy basis in the United States is practically intact, from the sun to wind to biofuels. And, because these alternative energy sources are regenerated organically...

why does the sun appear reddish during sunrise?

At the time of sunset or sunrise, the Sun and its surroundings appear red because of the scattering of light. At the time of sunset or sunrise, the light rays from the Sun have to travel a long...

Why is the series arrangement not used for domestic circuit?

The quantity of current in a serial circuit reduces when each component receives a low voltage, causing the gadget to become heated and malfunction. As a result, in home circuits, the series layout...

State the laws of refraction of light.

According to refraction laws, At the point of incidence, the incident ray, refracted ray, and normal to the interface of two media all lie on the same plane. A constant is the ratio of the sine of...

With the help of an experiment show that chlorophyll is essential for photosynthesis.

1. We'll start with a potted plant like a croton, which has partially green and partially white leaves. Chlorophyll is present in the green portion of the leaf, but not in the white portion. 2....

What is the role of decomposers in the ecosystem?

Decomposers have a variety of roles in the ecosystem: they decompose biodegradable substances into usable chemicals; they release nutrients into the soil by dissolving dead and decaying waste,...

What are the benefits of sexual reproduction in comparison to asexual reproduction?

The benefits of sexual reproduction include the generation of genetic variety in the progeny. Because of their diversity, the species can adapt to different habitats, giving them a survival...

What do you understand by elevation of boiling point and molal elevation constant, with the help of this constant how can you find the molecular mass of non-volatile solute

The elevation of boiling point on adding one mole solute to 1000 g solvent is called molal boiling point elevation constant. It is denoted by Kb. Its unit is K kg mol-1. The elevation of boiling...

Define excretion. What are excretory products?

Excretion is a vital life mechanism that is observed in all living organisms. Excretory products are produced as a result of both metabolic and non-metabolic processes. Animal wastes are divided...

Give the names of active ingredients and their one use of the following medicinal plants.
(i) Amla
(ii) Haldi
(iii) Tulsi

(i) Vitamin C – Cures fever, asthma and diabetes. (ii) Curcumin – Used as an antiseptic and antibiotic. (iii) Cineole and Eugenol – Cures skin diseases, ear pain, cough and cold

Write any two differences between respiration and combustion. $21 \mathrm{C}_{7038-\mathrm{C}_{13}}$

The process through which nutrients are transformed into useable energy in a cell is known as cellular respiration. It's a biological process in which energy is released in stages as chemical...

Write short notes on Sushrut

Sushrut was a renowned surgeon of ancient India and author of the book Sushrut Samhita. He was the first physician to advocate what is today known as 'Caesarean operation'. He was also expert in...

What is photosynthesis ? Wnte its chemical equation.

The following is the photosynthesis equation: C6H12O6 + 6O2 = 6CO2 + 6H20 + (energy) Glucose and oxygen are made from carbon dioxide, water, and light energy.

What steps are important for forest conservation ?

Other key methods for forest conservation include: Legislation prohibiting the legislature from cutting down trees indiscriminately. Willingness of the government to prevent deforestation by...

Write the equation for the reaction of Plaster of Paris with water.

CaSO4.1/2H2O + 3/2H2O = CaSO4.2H2O is the chemical equation for the reaction of Plaster of Paris and water. Heat is released when plaster of Paris reacts with water and crystallises. Plaster of...

Give two names of artificial sweeteners

Aspartame and Saccharin

Water is liquid while hydrogen sulphide is a gas at normal temperature. Why?

In water, the oxygen is electronegative due to the intermolecular hydrogen bonding which is formed in the water molecules and exists in a liquid state. Whereas, the sulphur is less electronegative...

Write prevention (two) of corrosion

Prevention of Corrosion: (i) By coating metal surface with oil or grease: A thin layer of oil or grease is coated on the surface of the metal. (ii) By painting the metal surface: A layer of point is...

Write electrochemical theory of corrosion

Electrochemical theory of corrosion: A number of galvanic cells are formed in impure iron. In rusting of iron pure iron acts as an anode while impure part of iron acts as a cathode. A thin layer...

What do you understand by corrosion?

Corrosion is defined as the process by which the layers of undesired compounds are formed on the surface of the metal when exposed to the atmospheric conditions

10.07 gram of silver is obtained during the circulations of electric of 5 ampere upto 30 minutes in silver nitrate pot (cell). Find out electrochemical equivalent of silver. If chemical equivalent of hydrogen is 0.00001036 then will be equivalent weight of silver

Faraday’s first law of electrolysis states that the amount of any substance deposited or liberated at any electrode is directly proportional to the quantity of electricity passed through the...

What happens when:
(i) Ammonia reacts with formaldehyde
(ii) Acetic acid reacts with PCl5

(i) Urotropine is formed when ammonia reacts with formaldehyde. 6HCHO + 4NH3 → (CH2) 6N4 + 6H2O (ii) Acetyl chloride is produced when acetic acid reacts with PCl5. CH3COOH + PCl5 → CH3COCl + POCl3 +...

What happens when:
(i) Acetyl chloride is reduced with hydrogen in presence of barium sulphate associated with palladium.
(ii) Benzaldehyde boils with 45% NaOH

(i) Acetaldehyde is obtained when acetyl chloride is reduced with hydrogen in presence of barium sulphate associated with palladium. CH3 – COCl + 2H → CH3CHO + HCl (ii) Sodium benzoate and Benzoyl...

Describe the preparation of acetic acid through quick vinegar process in following points: (i) Method

Acetic acid preparation by Vinegar Quick process: An aqueous solution of ethyl alcohol is mixed with oxidized in the presence of the enzyme micro derma aceti. The wooden vat is fitted with two...

What is the reaction of diethyl ether with HI acid?