JEE Physics Current Electricity MCQs Set 28

Practice MCQs for JEE Physics Current Electricity

Access targeted multiple-choice questions for Current Electricity designed to align with the latest JEE academic syllabus for JEE Physics. These objective practice sets help students evaluate their conceptual understanding and improve exam readiness.

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Multiple Choice Questions

Question 1: When no current is passed through a conductor,
(a) the free electrons do not move
(b) the average speed of a free electron over a large period of time is not zero
(c) the average velocity of a free electron over a large period of time is zero
(d) the average of the velocities of all the free electrons at an instant is non-zero
Show Answer & Explanation

Answer: (c) the average velocity of a free electron over a large period of time is zero

Explanation:
1. The free electrons move randomly with large speeds.
2. Their velocities are in all directions, so the average velocity is zero, while the average speed is not.

Teacher's Note:
1. Random motion has zero mean velocity.

Question 2: The resistance of a wire at room temperature 30°C is found to be 10 Ω. Now to increase the resistance by 10%, the temperature of the wire must be [the temperature coefficient of resistance of the material is 0.002 per °C, with R = R₀(1 + αt)]
(a) 36°C
(b) 83°C
(c) 63°C
(d) 33°C
Show Answer & Explanation

Answer: (b) 83°C

Explanation:
1. R₃₀ = R₀(1 + 0.06) = 10, so R₀ = 9.434 Ω.
2. We need 11 = R₀(1 + 0.002T), which gives 1 + 0.002T = 1.166 and T ≈ 83°C.

Teacher's Note:
1. Use R₀ at 0°C.

Question 3: When a potential difference is applied across an electrolyte, Ohm's law is obeyed at
(a) zero potential
(b) very low potential
(c) negative potential
(d) high potential
Show Answer & Explanation

Answer: (b) very low potential

Explanation:
1. For an electrolyte the current is proportional to the voltage only when the applied voltage is small.

Teacher's Note:
1. Low voltage keeps it linear.

Question 4: If in the experiment of the Wheatstone bridge the positions of the cell and the galvanometer are interchanged, then the balance point will
(a) change
(b) remain unchanged
(c) depend on the internal resistance of the cell and the resistance of the galvanometer
(d) none of these
Show Answer & Explanation

Answer: (b) remain unchanged

Explanation:
1. The balance condition P/Q = R/S does not involve the cell or the galvanometer.
2. Interchanging them leaves the balance unchanged.

Teacher's Note:
1. Balance condition is symmetric.

Question 5: The drift velocity of electrons is due to
(a) motion of conduction electrons due to random collisions
(b) motion of conduction electrons due to the electric field E
(c) repulsion of the conduction electrons due to inner electrons of ions
(d) collision of conduction electrons with each other
Show Answer & Explanation

Answer: (b) motion of conduction electrons due to the electric field E

Explanation:
1. The drift velocity is the small average velocity gained under the electric field.
2. It is superposed on the random thermal motion.

Teacher's Note:
1. Drift is field-driven.

Question 6: A wire X is half the diameter and half the length of a wire Y of similar material. The ratio of the resistance of X to that of Y is
(a) 8 : 1
(b) 4 : 1
(c) 2 : 1
(d) 1 : 1
Show Answer & Explanation

Answer: (c) 2 : 1

Explanation:
1. R ∝ l/d².
2. R_X/R_Y = (1/2)/(1/2)² = 2.

Teacher's Note:
1. R ∝ l/d².

Question 7: The speed at which the current travels in a conductor is nearly
(a) \( 3\times10^{4}\ \text{m/s} \)
(b) \( 3\times10^{5}\ \text{m/s} \)
(c) \( 4\times10^{6}\ \text{m/s} \)
(d) \( 3\times10^{8}\ \text{m/s} \)
Show Answer & Explanation

Answer: (d) \( 3\times10^{8}\ \text{m/s} \)

Explanation:
1. The electric field that sets the electrons in motion propagates at nearly the speed of light.
2. So the current is established at about 3 × 10⁸ m/s.

Teacher's Note:
1. The signal travels at about c.

Question 8:
Assertion (A): The electric field outside a conducting wire which carries a constant current is zero.
Reason (R): The net charge on a conducting wire is zero.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation

Answer: (d) A is false, but R is true.

Explanation:
1. A current-carrying wire has an electric field outside it (as well as inside), so the assertion is false.
2. The wire is neutral overall, so the reason is true.

Teacher's Note:
1. Neutral does not mean no field.

Question 9: In a Wheatstone bridge all the four arms have equal resistance R. If the resistance of the galvanometer arm is also R, the equivalent resistance of the combination is
(a) 2R
(b) \( R/4 \)
(c) \( R/2 \)
(d) R
Show Answer & Explanation

Answer: (d) R

Explanation:
1. The bridge is balanced, so no current flows through the galvanometer arm.
2. The equivalent resistance is (2R × 2R)/(4R) = R.

Teacher's Note:
1. Balanced bridge.

Question 10: At temperature 0 K, germanium behaves as a/an
(a) conductor
(b) insulator
(c) super-conductor
(d) ferromagnetic
Show Answer & Explanation

Answer: (b) insulator

Explanation:
1. At 0 K no electrons are in the conduction band of germanium.
2. So it behaves as an insulator.

Teacher's Note:
1. Semiconductors are insulators at 0 K.

Question 11: Two wires A and B of the same material, having radii in the ratio 1 : 2, carry currents in the ratio 4 : 1. The ratio of the drift speeds of electrons in A and B is
(a) 16 : 1
(b) 1 : 16
(c) 1 : 4
(d) 4 : 1
Show Answer & Explanation

Answer: (a) 16 : 1

Explanation:
1. v_d = I/(nAe) ∝ I/r².
2. The ratio is (4/1²) : (1/2²) = 4 : 1/4 = 16 : 1.

Teacher's Note:
1. v_d ∝ I/r².

Question 12: When a potential difference V is applied across a conductor at a temperature T, the drift velocity of electrons is proportional to
(a) \( \sqrt V \)
(b) \( V \)
(c) \( \sqrt T \)
(d) \( T \)
Show Answer & Explanation

Answer: (b) \( V \)

Explanation:
1. v_d = eEτ/m and E = V/l.
2. So v_d is proportional to V.

Teacher's Note:
1. v_d ∝ E.

Question 13: Match Column I with Column II.
Column IColumn II
(A) Ohm's law is applicable to(1) Metals
(B) Ohm's law is not applicable to(2) Greater resistivity
(C) Alloys have(3) Diodes, electrolytes, semiconductors
(D) A heat-sensitive resistor(4) Thermistors

(a) A-1, B-2, C-3, D-4
(b) A-3, B-1, C-2, D-4
(c) A-1, B-3, C-2, D-4
(d) A-1, B-4, C-2, D-3
Show Answer & Explanation

Answer: (c) A-1, B-3, C-2, D-4

Explanation:
1. Metals obey Ohm's law (A-1).
2. Diodes, electrolytes and semiconductors do not (B-3).
3. Alloys have greater resistivity than metals (C-2).
4. A heat-sensitive resistor is a thermistor (D-4).

Teacher's Note:
1. Ohmic and non-ohmic materials.

Question 14: Match Column I with Column II.
Column IColumn II
(A) Silver(1) Wire-bound resistor
(B) Semiconductor(2) Resistor of higher range
(C) Carbon resistor(3) Negative temperature coefficient of resistivity
(D) Manganin(4) Least resistivity

(a) A-4, B-2, C-3, D-1
(b) A-4, B-3, C-2, D-1
(c) A-1, B-3, C-2, D-4
(d) A-3, B-4, C-2, D-1
Show Answer & Explanation

Answer: (b) A-4, B-3, C-2, D-1

Explanation:
1. Silver has the least resistivity (A-4).
2. Semiconductors have a negative temperature coefficient (B-3).
3. Carbon resistors cover higher resistance ranges (C-2).
4. Manganin is used for wire-wound resistors (D-1).

Teacher's Note:
1. Material properties.

Question 15: A metre bridge is set up to determine an unknown resistance X (in the left gap) using a standard 10 ohm resistor (in the right gap). The galvanometer shows a null point when the tapping key is at the 52 cm mark. The end corrections are 1 cm and 2 cm respectively for the ends A and B. The determined value of X is
(a) 10.2 ohm
(b) 10.6 ohm
(c) 10.8 ohm
(d) 11.1 ohm
Show Answer & Explanation

Answer: (b) 10.6 ohm

Explanation:
1. The effective lengths are 52 + 1 = 53 cm on the left and 48 + 2 = 50 cm on the right.
2. X = 10 × 53/50 = 10.6 Ω.

Teacher's Note:
1. Add the end corrections.

Question 16: In the series combination of two or more than two resistances,
(a) the current through each resistance is the same
(b) the voltage through each resistance is the same
(c) neither current nor voltage through each resistance is the same
(d) both current and voltage through each resistance are the same
Show Answer & Explanation

Answer: (a) the current through each resistance is the same

Explanation:
1. The same current flows through all the resistors in series, and the voltage divides.

Teacher's Note:
1. Series: same current.

Question 17: The number of free electrons per cubic metre in a metallic conductor is of the order of
(a) \( 10^{22} \)
(b) \( 10^{24} \)
(c) \( 10^{26} \)
(d) \( 10^{28} \)
Show Answer & Explanation

Answer: (d) \( 10^{28} \)

Explanation:
1. Metals have roughly one free electron per atom, about 10²⁸ per m³.

Teacher's Note:
1. n ≈ 10²⁸ m⁻³.

Question 18:
Assertion (A): In a metre bridge experiment, a high resistance is always connected in series with a galvanometer.
Reason (R): As the resistance increases, the current through the circuit increases.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation

Answer: (c) A is true, but R is false.

Explanation:
1. A high series resistance protects the galvanometer from large currents, so the assertion is true.
2. A larger resistance reduces the current, so the reason is false.

Teacher's Note:
1. Series resistance limits current.

Question 19: Ohm's law fails in which of the following cases? I. Potential V depends on I non-linearly. II. The relation between V and I depends on the sign of V for the same absolute value of V. III. V depends on I linearly.
(a) I only
(b) II only
(c) I and III
(d) I and II
Show Answer & Explanation

Answer: (d) I and II

Explanation:
1. Ohm's law needs V to be linear in I and independent of the sign of V.
2. It fails when V is non-linear in I (I) or when the relation depends on the sign of V (II).

Teacher's Note:
1. Ohm's law means linear and symmetric.

Question 20: A potentiometer wire of length 1 m is connected in series with a 490 Ω resistance and a 2 V battery. If the potential gradient is 0.2 mV/cm, the resistance of the potentiometer wire is
(a) 4.9 Ω
(b) 7.9 Ω
(c) 5.9 Ω
(d) 6.9 Ω
Show Answer & Explanation

Answer: (a) 4.9 Ω

Explanation:
1. The p.d. across the wire is 0.2 mV/cm × 100 cm = 20 mV.
2. 2R/(490 + R) = 0.02 gives R ≈ 4.95 Ω, nearest to 4.9 Ω.

Teacher's Note:
1. V_wire = IR.

Question 21: In a conductor, when electrons move between two collisions, their paths are ____ A ____ when external fields are absent and ____ B ____ when an external field is present. A and B refer to
(a) straight lines, straight lines
(b) straight lines, curved lines
(c) curved lines, straight lines
(d) curved lines, curved lines
Show Answer & Explanation

Answer: (b) straight lines, curved lines

Explanation:
1. With no field the electron moves in a straight line between collisions.
2. With a field it accelerates, so the path becomes curved.

Teacher's Note:
1. Field bends the path.

Question 22: We are able to obtain fairly large currents in a conductor because
(a) the electron drift speed is usually very large
(b) the number density of free electrons is very high and this can compensate for the low value of the electron drift speed and the very small magnitude of the electron charge
(c) the number density of free electrons as well as the electron drift speeds are very large and these compensate for the very small magnitude of the electron charge
(d) the very small magnitude of the electron charge has to be divided by the still smaller product of the number density and drift speed to get the electric current
Show Answer & Explanation

Answer: (b) the number density of free electrons is very high and this can compensate for the low value of the electron drift speed and the very small magnitude of the electron charge

Explanation:
1. I = nAev_d.
2. The huge number density n compensates for the small drift speed and small charge e.

Teacher's Note:
1. I = nAev_d.

Question 23: The electric field intensity E, the current density J and the specific resistance k are related to each other through the relation
(a) \( E=J/k \)
(b) \( E=Jk \)
(c) \( E=k/J \)
(d) \( k=JE \)
Show Answer & Explanation

Answer: (b) \( E=Jk \)

Explanation:
1. E = ρJ.
2. With ρ = k, E = Jk.

Teacher's Note:
1. E = ρJ.

Question 24: In a metre bridge or a Wheatstone bridge for measurement of resistance, the known and the unknown resistances are interchanged. The error so removed is
(a) end correction
(b) index error
(c) due to temperature effect
(d) random error
Show Answer & Explanation

Answer: (a) end correction

Explanation:
1. Interchanging the resistances and averaging eliminates the error due to the end resistances (end correction).

Teacher's Note:
1. Interchange removes end error.

Question 25:
Assertion (A): Bending a wire does not affect its electrical resistance.
Reason (R): The resistance of a wire is proportional to the resistivity of the material.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation

Answer: (b) Both A and R are true, but R is not the correct explanation of A.

Explanation:
1. R = ρl/A depends only on the material, length and area, not on the shape.
2. The reason is true but does not by itself explain why shape is irrelevant.

Teacher's Note:
1. R = ρl/A.

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