Physics

### a) Consider the circuit in the figure. How much energy is absorbed by electrons from the initial state of no current to the state of drift velocity? b) Electrons give up energy at the rate of RI2 per second to the thermal energy. What time scale would one associate with energy in problem a) n = no of electron/volume = 1029/m3, length of circuit = 10 cm, cross-section = A = 1mm2

a) Current is given as I = V/R from the Ohm’s law Therefore, I = 1A But, I = ne Avd vd = I/neA When the values for the above parameters are substituted, vd = 1/1.6 × 10-4 m/s The KE = (KE of one...

### In an experiment with a potentiometer, VB = 10V. R is adjusted to be 50 Ω. A student wanting to measure voltage E1 of a battery finds no null point possible. He then diminishes R to 10 Ω and is able to locate the null point on the last segment of the potentiometer. Find the resistance of the potentiometer wire and potential drop per unit length across the wire in the second case.

Equivalent resistance of the potentiometer = 50 Ohm + R’ Equivalent voltage across the potentiometer = 10 V Current through the main circuit I = 10/(50 Ohms +R’) Potential difference across wire of...

### A room has AC run for 5 hours a day at a voltage of 220V. The wiring of the room consists of Cu of 1 mm radius and a length of 10 m. Power consumption per day is 10 commercial units. What fraction of it goes in the joule heating in wires? What would happen if the wiring is made of aluminium of the same dimensions?

Power consumption in a day = 10 units Power consumption per hour = 2 units Power consumption = 2 units = 2 kW = 2000 J/s Power consumption in resistors, P = VI Which gives I = 9A We know that...

### Two cells of voltage 10V and 2V and internal resistances 10Ω and 5Ω respectively are connected in parallel with the positive end of the 10V battery connected to the negative pole of 2V battery. Find the effective voltage and effective resistance of the combination.

Kirchhoff’s law is applied at c, I1 = I + I2 Kirchhoff’s law is applied at efbae, 10 – IR – 10I2 = 0 10 = IR + 10I1 Kirchhoff’s law is applied at cbadc, -2-IR+5I2 = 0 2 = 5I2- RI I2 = I1 – I...

### Suppose there is a circuit consisting of only resistances and batteries and we have to double all voltages and all resistances. Show that currents are unaltered.

Reff is the equivalent internal resistance of the battery Veff is the equivalent voltage of the battery Using Ohm’s law, I = Veff/(Reff + R) When the resistance and effective voltage are increased...

### Two conductors are made of the same material and have the same length. Conductor A is a solid wire of diameter 1 mm. Conductor B is a hollow tube of outer diameter 2 mm and inner diameter 1 mm. Find the ratio of resistance RA to RB.

Resistance of wire R = ρ l/A Where A is the cross-sectional area of the conductor L is the length of the conductor ρ is the specific resistance RA = ρl/π(10-3 × 0.5)2 RB = ρl/ π[10-3)2 × (0.5 ×...

### The circuit in the figure shows two cells connected in opposition to each other. Cell E1 is of emf 6V and internal resistance 2Ω; the cell E2 is of emf 4V and internal resistance 8 Ω. Find the potential difference between the points A and B.

Applying Ohm’s law, equivalent emf of the two cells = 6 – 4 = 2V Equivalent resistance = 2 + 8 = 10 Ω Electric current, I = 6-4/2+8 = 0.2A When the loop is considered in the anti-clockwise...

### Two cells of same emf E but internal resistance r1 and r2 are connected in series to an external resistor R. What should be the value of R so that the potential difference across the terminals of the first cell becomes zero.

Effective emf of two cells = E + E = 2E Effective resistance = R + r1 + r2 Electric current is given as I = 2E/R+r1+r2 Potential difference is given as V1 – E – Ir1 = 0 Which f=gives R = r1 –...

### Let there be n resistors R1……..Rn with Rmax = max(R1……Rn) and Rmin = min(R1…….Rn). Show that when they are connected in parallel, the resultant resistance Rp < Rmin and when they are connected in series, the resultant resistance Rs > Rmax. Interpret the result physically.

The current is represented as I = E/R+nR when the resistors are connected in series. Current is expressed as 10I = E/(R+R/n) when the resistors are connected in parallel....

### . A cell of emf E and internal resistance r is connected across an external resistance R. Plot a graph showing the variation of PD across R versus R.

The graphic depiction is as follows: The resistance r is connected across the external resistance R, and E is the cell's emf.  V = ER/R+r is the connection between voltage and R....

### While doing an experiment with potentiometer it was found that the deflection is one-sided and i) the deflection decreased while moving from one end A of the wire to the end B; ii) the deflection increased, while the jockey was moved towards the end B. i) Which terminal +ve or –ve of the cell E, is connected at X in case i) and how is E1 related to E? ii) Which terminal of the cell E1 is connected at X in case ii)?

The positive terminal of cell E1 is linked to E, and E is connected to X.  Furthermore, E1 > E ii) cell E1's negative terminal is linked to X.

### Power P is to be delivered to a device via transmission cables having resistance Rc. If V is the voltage across R and I the current through it, find the power wasted and how can it be reduced.

P = i2Rc is the power utilised by transmission lines. The resistance of connecting wires is denoted by Rc. P = VI is the formula for calculating power. Power...

### Power P is to be delivered to a device via transmission cables having resistance Rc. If V is the voltage across R and I the current through it, find the power wasted and how can it be reduced.

Power consumed by the transmission lines is given as P = i2Rc. Where Rc is the resistance of connecting cables. Power is given as P = VI. The transmission of power takes places either during low...

### Why are alloys used for making standard resistance coils?

Alloys are used in the making of the standard resistance coils because they have less temperature coefficient of resistance and the temperature sensitivity is also less.

### For wiring in the home, one uses Cu wires or Al wires. What considerations are involved in this?

The main considerations in the selection of the wires is the conductivity of the metal, cost of metal, and their availability.

### What are the advantages of the null-point method in a Wheatstone bridge? What additional measurements would be required to calculate R unknown by any other?

The advantage of a null-point in the Wheatstone bridge is that the resistance of the galvanometer is not affected by the balance point. The R unknown is calculated by using Kirchhoff’s rule.

### The relaxation time τ is nearly independent of applied E field whereas it changes significantly with temperature T. First fact is responsible for Ohm’s law whereas the second fact leads to a variation of ρ with temperature. Elaborate why?

Relaxation time is the time interval between two successive collisions of the electrons.It is defined asτ = mean free path/rms velocity of electrons usually, the drift velocity of the electrons is...

### Is the momentum conserved when charge crosses a junction in an electric circuit? Why or why not?

The momentum is not conserved when the charge crosses a junction in an electric circuit. This is because the drift velocity is proportional to the electric field.

### In a meter bridge, the point D is a neutral point.a) the meter bridge can have no other neutral point for this set of resistances b) when the jockey contacts a point on meter wire left of D, current flows to B from the wire c) when the jockey contacts a point on a meter wire to the right of D, current flows from B to the wire through the galvanometer d) when R is increased, the neutral point shifts to left

The correct answer is a) the meter bridge can have no other neutral point for this set of resistances c) when the jockey contacts a point on a meter wire to the right of D, current flows from B to...

### The measurement of an unknown resistance R is to be carried out using Wheatstone bridge. Two students perform an experiment in two ways. The first student take R2 = 10Ω and R1 = 5Ω. The other student takes R2 = 1000 Ω and R1 = 500 Ω. In the standard arm, both take R3 = 5 Ω. Both find R = R2/R1 R3 = 10 Ω within errors. a) the errors of measurement of the two students are the same b) errors of measurement do depend on the accuracy with which R2 and R1 can be measured c) if the student uses large values of R2 and R1, the currents through the arms will be feeble. This will make determination of null point accurately more difficult d) Wheatstone bridge is a very accurate instrument and has no errors of measurement

The correct answer is b) errors of measurement do depend on the accuracy with which R2 and R1 can be measured c) if the student uses large values of R2 and R1, the currents through the arms will be...

### Temperature dependence of resistivity ρ(T) of semiconductors, insulators, and metals is significantly based on the following factors: a) number of charge carriers can change with temperature T b) time interval between two successive collisions can depend on T c) length of material can be a function of T d) mass of carriers is a function of T

solution:The correct answer is a) number of charge carriers can change with temperature T b) time interval between two successive collisions can depend on T

### Consider a simple circuit in the figure.stands for a variable resistance R’.R’ can vary from R0 to infinity. r is internal resistance of the battery, a) potential drop across AB is nearly constant as R’ is varied b) current through R’ is nearly a constant as R’ is varied c) current I depends sensitively on R’ d) I ≥V/r+R always

solution: The correct answer is a) potential drop across AB is nearly constant as R’ is varied d) I ≥V/r+R always

### Kirchhoff’s junction rule is a reflection of a) conservation of current density vector b) conservation of charge c) the fact that the momentum with which a charged particle approaches a junction is unchanged as the charged particle leaves the junction d) the fact that there is no accumulation of charges at a junction

solution: The correct answer is b) conservation of charge d) the fact that there is no accumulation of charges at a junction

### Which of the following characteristics of electrons determines the current in a conductor? v a) drift velocity alone b) thermal velocity alone c) both drift velocity and thermal velocity d) neither drift nor thermal velocity

solution: The correct answer is a) drift velocity alone

### A metal rod of length 10 cm and a rectangular cross-section of 1 cm × 1/2 cm is connected to battery across opposite faces. The resistance will be a) maximum when the battery is connected across 1 cm × 1/2 cm faces b) maximum when the battery is connected across 10 cm × 1 cm faces c) maximum when the battery is connected across 10 cm × 1/2 cm faces d) same irrespective of the three faces

solution:The correct solution is a) maximum when the battery is connected across 1 cm × 1/2 cm faces

### Two cells of emf’s approximately 5V and 10V are to be accurately compared using a potentiometer of length 400 cm. a) the battery that runs the potentiometer should have voltage of 8V b) the battery of potentiometer can have a voltage of 15V and R adjusted so that the potential drop across the wire slightly exceeds 10V c) the first portion of 50 cm of wire itself should have a potential drop of 10V d) potentiometer is usually used for comparing resistances and not voltages

Solution: The correct solution is b) the potentiometer's battery can be set to 15V and R adjusted so that the potential drop across the wire is a little higher than 10V.

### A resistance R is to be measured using a meter bridge. Student chooses the standard resistance S to be 100Ω. He finds the null point at l1 = 2.9 cm . He is told to attempt to improve the accuracy. Which of the following is a useful way? a) he should measure l1 more accurately b) he should change S to 1000 Ω and repeat the experiment c) he should change S to 3 Ω and repeat the experiment d) he should give up hope of a more accurate measurement with a meter bridge

solution:The correct answer is c) he should change S to 3 Ω and repeat the experiment

### Two batteries of emf ε1 and ε2 and internal resistances r1 and r2 respectively are connected in parallel as shown in the figure.a) the equivalent emf εeq of the two cells is between ε1 and ε2 that is ε1 < εeq < ε2 b) the equivalent emf εeq is smaller than ε1 c) the εeq is given by εeq = ε1 + ε2 always d) εeq is independent of internal resistances r1 and r2

solution: The correct answer is a) the equivalent emf εeq of the two cells is between ε1 and ε2 that is ε1 < εeq < ε2

### Consider a current-carrying wire in the shape of a circle. Note that as the current progresses along the wire, the direction of j changes in an exact manner, while the current I remain unaffected. The agent that is essentially responsible for is a) source of emf b) electric field produced by charges accumulated on the surface of wire c) the charges just behind a given segment of wire which push them just the right way by repulsion d) the charges ahead

solution: The correct answer is b) electric field produced by charges accumulated on the surface of wire

### When a beam of unpolarised monochromatic light is incident on a plane glass plate at a polarising angle, then which one of the following statements is correct?A) Reflected and refracted rays are completely polarised with their planes of polarisation perpendicular to each other.B) Reflected light is partially polarised but refracted light is plane polarised.C) Reflected and refracted rays are completely polarised with their planes of polarisation parallel to each other.D) Reflected light is plane polarised light but transmitted light is partially polarised.

Correct option is D.

### Five capacitors each of capacitance ‘ are connected as shown in the figure. The ratio of equivalent capacitance between and and the equivalent capacitance between and is

A)$2: 3$ B)$1: 1$ C)$3: 1$ D)$5: 2$ Correct option is A. For the both cases the equivalent circuits are shown in figure. For (1) the equivalent capacitance between $\mathrm{P}$ and $\mathrm{R}$ is...

### What is the stopping potential, when a metal surface with work function is illuminated with light of energy ?A) B)C)D)

Correct option is D. $\begin{array}{l} e V s=E-W_{0} \\ \therefore V_{s}=\frac{E}{e}-\frac{W_{0}}{e}=\frac{3 e}{e}-\frac{1.2 e V}{e}=1.8 V \end{array}$

### An ideal gas occupies a volume ‘ ‘ at a pressure ‘ ‘ and absolute temperature . The mass of each molecule is ‘ ‘. If ‘ is the Boltzmann’s constant, then the density of gas is given by expressionA)B)C)D)

Correct option is D. The ideal gas law is given by $\mathrm{PV}=\mathrm{nRT}$, where $\mathrm{n}$ is the number of moles of a gas. $\mathrm{n}=$ mass of the gas $/$ molecular weight of the gas....

### In communication with the help of antenna, the range covered (for the line of sight propagation) is initially ‘ ‘. If the height of antenna is doubled, the range covered would becomeA)B) C) D)

Correct option is A. Range of antenna $=d \sqrt{2 \mathrm{hr}}, \mathrm{h}=$ height of antenna, $\mathrm{R}=$ radius of earth if $\mathrm{h}$ is doubled i.e., $\mathrm{h}^{\prime}=2 \mathrm{~h}$,...

### In suspended type of moving coil galvanometerA) coil is stationary.B) magnet is stationary.C) magnet and coil are stationary.D) magnet and coil are moving.

Correct option is B.

### The effective length of a magnet is and its pole strength is . The magnetic moment, if it is bent in the form of a semicircle is A) B)C) D)

Correct option is C $0.16$ The effective length of magnet $=31.4 \mathrm{~cm}$ Pole strength $\mathrm{m}=0.8 \mathrm{Am}$ Length of semi-circle $=\pi \frac{\mathrm{D}}{2}=1$ where, $\mathrm{D}=$...

### For which one of the following, Bhor model is not valid? (1) Deuteron atom (2) Singly ionised neon atom (Ne ) (3) Hydrogen atom (4) Singly ionised helium atom (

Correct option (2) The Bohr Model is only valid for atoms with one electron in orbit.

### A long solenoid of length having 100 turns carries a current of . The magnetic field at the centre of the solenoid is: ) (1) (2) (3) (4)

Correct option is 3) Magnetic field for solenoid is given by formula $\mathrm{B}=\mu_{0} \mathrm{nI}$ $\mathrm{n}=\frac{\mathrm{N}}{\ell}$ Evaluating, $=4 \pi \times 10^{-7} \times 200 \times 2.5$...

### The ratio of contributions made by the electric field and magnetic field components to the intensity of an electromagnetic wave is : speed of electromagnetic waves) (1) (2) (3) c: 1 (4)

Correct option: 4) Because the energy distribution is the same, The electric-to-magnetic-field ratio will be $1:1$.

### Which of the following graph represents the variation of resistivity ( ) with temperature (T) For copper?

The correct option is 1) As we know that the Relation between resistivity and temperature is given by $\rho=\rho_{0} e^{-\alpha T}$

### For the logic circuit shown, the truth table is :

Correct option is 3) According to de-Morgan rule, $\overline{\bar{A}+\bar{B}}=\overline{\bar{A}} \cdot \overline{\bar{B}}=A \cdot B$

### A ball is thrown vertically downward with a velocity of from the top of a tower. It hits the ground after some time with a velocity of . The height of the tower is : (1) (2) (3) (4)

Correct option: 2) Using the equation of motion, $v^{2}-u^{2}=2 a s$ Substituting and calculating the value, $(80)^{2}-(-20)^{2}=2(-10) \times s$ $6400-400=2 \times(-10) \times s$...

### The mean free path for a gas, with molecular diameter and number density can be expressed as : (1) (2) (3) (4)

Correct option: 4) In physics, the mean free path is the average distance over which a moving particle's direction or energy changes significantly, usually as a result of one or more successive...

### A cylinder contains hydrogen gas at pressure of and temperature . Its density is : (1) (2) (3) (4)

Correct option: 4) Using the ideal gas equation, we evaluate the value of density by making modification,  \begin{aligned} &\therefore PV = nRT \\ &\Rightarrow PV =\frac{ m }{ M } RT \quad...

### In a certain region of space with volume 0.2 cubic meters, the electric potential is found to be 5 V throughout. The magnitude of electric field in this region is : (1) 1 N/C (2) 5 N/C (3) Zero (4) 0.5 N/C

Correct option: 3) Given $v=$ const. (5 volt) $As E =-\frac{ dv }{ dr }$ So differentiation of a constant is zero, thus, $E =0$

### Two bodies of mass 4 kg and 6 kg are tied to the ends of a massless string. The string passes over a pulley which is frictionless (see figure). The acceleration of the system in terms of acceleration due to gravity (g) is : (1) g/5 (2) g/10 (3) g (4) g/2

Correct option: 1) According to the figure, the force equation on both the blocks are, 6g – T = 6a T – 4g = 4a Solving both we get the value of a = g/5 $m/s^2$

### A spherical conductor of radius has a charge of distributed uniformly. what is the magnitude of electric field at a point from the centre of the sphere?

Answer: option 4 As we know the formula for electric field, so evaluating according to given info, $E=\frac{k Q}{r^{2}}=\frac{9 \times 10^{9} \times 3.2 \times 10^{-7}}{15 \times 15 \times 10^{-4}}$...

### For transistor action, which of the following statements is correct ? (1) Both emitter junction as well as the collector junction are forward biased. (2) The base region must be very thin and lightly doped. (3) Base, emitter and collector regions should have same doping concentrations. (4) Base, emitter and collector regions should have same size.

Correct option: 2) The base junction must be lightly doped for transistor action, resulting in a very thin base region.

### Match the corresponding entries of column 1 with column 2. [Where is the magnification produced by the mirror] A and and and and B and and and b; and C and and and and D and and and and

Correct Option A Answer: The term "positive magnification" refers to an image that is upright in relation to the object. Negative magnification refers to an image that is inverted in relation to the...

Correct Option B Solution: For vertical equilibrium on the curved road we have, $N \cos \theta=m g+f_{1} \operatorname{Sin} \theta----(1)$ Forhorizontal equilibrium on the curved road we have,...
Correct Option B Solution: In AC circit the power is given by formula, $P=V I \operatorname{Cos} \phi$ Because the phase difference in a purely capacitive circuit is 90 degrees, no power is...