Lakhmir Singh

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...

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 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...

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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...

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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...

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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 ×...

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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...

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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 –...

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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....

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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.

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Compound ‘A’ was prepared by oxidation of compound ‘B’ with alkaline KMnO4. Compound ‘A’ on reduction with lithium aluminium hydride gets converted back to compound ‘B’. When compound ‘A’ is heated with compound B in the presence of H2SO4 it produces the fruity smell of compound C to which family the compounds ‘A’, ‘B’ and ‘C’ belong to?

Solution: Compound ‘A’ belongs to the carboxylic acid. Compound ‘B’ belongs to alcohol. Compound ‘C’ belongs to an ester group.

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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...

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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

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

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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...

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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...

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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

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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  

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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

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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

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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.

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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

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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

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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

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The correct order of increasing acidic strength is _____________. (i) Phenol < Ethanol < Chloroacetic acid < Acetic acid (ii) Ethanol < Phenol < Chloroacetic acid < Acetic acid (iii) Ethanol < Phenol < Acetic acid < Chloroacetic acid (iv) Chloroacetic acid < Acetic acid < Phenol < Ethanol

Solution: Option (iii) is the answer. Reason: The correct order of increasing acidic strength is Ethanol < Phenol < Acetic acid < Chloroacetic acid. Phenol is more acidic than ethanol...

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Under which of the following reaction conditions, aniline gives p-nitro derivative as the major product?
(i) Acetyl chloride/pyridine followed by reaction with conc. H2SO4 + conc. HNO3
(ii) Acetic anhydride/pyridine followed by conc. H2SO4 + conc. HNO3
(iii) Dil. HCl followed by reaction with conc. H2SO4 + conc. HNO3
(iv) Reaction with conc. HNO3 + conc.H2SO4

Solution: Option (i) and (ii) are the answers. Reason: In addition to the nitro derivatives, direct nitration of aniline produces tarry oxidation products. Furthermore, in a strongly acidic...

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Which of the following methods of preparation of amines will not give the same number of carbon atoms in the chain of amines as in the reactant?
(i) The reaction of nitrite with LiAlH4.
(ii) The reaction of the amide with LiAlH4 followed by treatment with water.
(iii) Heating alkyl halide with potassium salt of phthalimide followed by hydrolysis.
(iv) Treatment of amide with bromine in the aqueous solution of sodium hydroxide.

Solution: Option (iv) is the answer. Reason: In Hoffmann Bromide degradation as the word, suggest, the amide is reduced to an amine with 1- carbonless, so this is the method in which we don't get...

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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.

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The moment of inertia of a ring about an axis passing through the centre and perpendicular to its plane is ‘I’. It is rotating with angular velocity ^{\prime} \omega^{\prime} . Another identical ring is gently placed on it so that their centres coincide. If both the rings are rotating about the same axis then loss is kinetic energy is
A) \frac{\mathrm{I} \omega^{2}}{2}
B) \frac{\mathrm{I} \omega^{2}}{4}
C) \frac{\mathrm{I} \omega^{2}}{6}
D) \frac{\mathrm{I} \omega^{2}}{8}

Correct option is B $\frac{\mathrm{I} \omega^{2}}{4}$ Initial angular momentum, $\mathrm{L}_{1}=\mathrm{I} \omega$ $\mathrm{K}_{1}=\frac{1}{2} \mathrm{I} \omega^{2}$ When, second ring is put on it...

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Two cylinders A and B of equal capacity are connected to each other via a stop cock. A contains an ideal gas at standard temperature and pressure. B is completely evacuated. The entire system is thermally insulated. The stop cock is suddenly opened. The process is :
(1) isochoric
(2) isobaric
(3) isothermal
(4) adiabatic

Correct option (4) When cock is removed, dQ = 0 for the thermally insulated system. Because dw = 0 in vacuum Walls that are thermally insulated du + dw = dQ So du also a zero.

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Identify the correct statement from the following :
(1) Blister copper has blistered appearance due to evolution of CO2.
(2) Vapour phase refining is carried out for Nickel by Van Arkel method.
(3) Pig iron can be moulded into a variety of shapes.
(4) Wrought iron is impure iron with 4% carbon.

Correct option: (3) Explanation: Because of the evolution of $SO_2$, not $CO_2$, blister copper has a blistered appearance. The Van Arkel method is used to obtain ultra-pure Titanium through vapor...

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