Electric Current, Drift Velocity and Mobility – Electric current: NEET MCQs with Answers

13 free questions on Electric Current, Drift Velocity and Mobility – Electric current for NEET (UG), starting with previous-year NEET and AIPMT questions. Try each one, then tap Show answer for the answer and a short explanation.

Syllabus covered: Electric current. Drift velocity, mobility and their relation with electric current

Practise all 51 Electric Current, Drift Velocity and Mobility – Electric current questions free Take a free timed test

Question 1

Previous-year question
A charged particle drifting with a velocity of 7.5 × 10⁻⁴ m s⁻¹ in an electric field of 3 × 10⁻¹⁰ V m⁻¹ possesses a mobility (in m² V⁻¹ s⁻¹) of [NEET 2020]
  1. 2.5 × 10⁶
  2. 2.5 × 10⁻⁶
  3. 2.25 × 10⁻¹⁵
  4. 2.25 × 10¹⁵
Show answer
Answer: (A) 2.5 × 10⁶
Explanation: Mobility is defined as drift velocity per unit electric field, μ = v_d/E. Hence μ = (7.5 × 10⁻⁴)/(3 × 10⁻¹⁰) = 2.5 × 10⁶ m² V⁻¹ s⁻¹.

Question 2

Wires P and Q of the same metal, at the same temperature, have lengths L and 3L and radii r and 2r respectively. They are connected in parallel across a cell of negligible internal resistance. The ratio of the drift speed of electrons in P to that in Q is
  1. 1 : 3
  2. 3 : 1
  3. 3 : 4
  4. 4 : 3
Show answer
Answer: (B) 3 : 1
Explanation: Drift speed is v_d = eEτ/m, and the field in a wire is E = V/L. With the same material and temperature, τ is the same, and the voltage is the same across both wires, so v_d is proportional to 1/L and does not depend on the radius. The ratio is therefore 3 : 1. The currents are in a different ratio, 3 : 4, because the areas also differ.

Question 3

A wire of metal P with diameter 1 mm and a wire of metal Q with diameter 2 mm are joined end to end and carry a steady current. The free-electron density of P is 1.5 times that of Q. What is the ratio of the drift speed in wire P to the drift speed in wire Q?
  1. 6 : 1
  2. 8 : 3
  3. 3 : 8
  4. 2 : 3
Show answer
Answer: (B) 8 : 3
Explanation: The wires are in series, so the current I = neAv is the same in both. Hence v is proportional to 1/(nA). The ratio is v(P)/v(Q) = [n(Q)/n(P)] × [A(Q)/A(P)] = (1/1.5) × 4 = 8/3.

Question 4

In a torch, 30 cm of connecting wire lies between the switch and the bulb, and the free electrons in it drift at about 0.1 mm/s. About how long would an electron take to drift from the switch to the bulb, and why does the bulb glow almost at once when the switch is closed?
  1. About 50 min; electrons near the switch reach the bulb within microseconds at their thermal speed of about 10⁵ m/s
  2. About 5 min; electrons near the switch reach the bulb first at their thermal speed of about 10⁵ m/s
  3. About 50 s; the drift speed becomes very large at the moment the switch is closed
  4. About 50 min; the electric field is set up along the whole circuit at nearly the speed of light, so electrons everywhere begin to drift at once
Show answer
Answer: (D) About 50 min; the electric field is set up along the whole circuit at nearly the speed of light, so electrons everywhere begin to drift at once
Explanation: The drift time is t = 0.30 m ÷ (1 × 10⁻⁴ m/s) = 3000 s, or about 50 minutes. The bulb does not wait for these electrons. The electric field spreads through the closed circuit at nearly the speed of light, so free electrons already in the filament start drifting almost immediately. Thermal motion is random and carries no net charge along the wire.

Question 5

Charge carrier P has charge e, mass m and mean time between collisions τ. Charge carrier Q has charge 3e, mass 2m and mean time between collisions τ/2. What is the ratio of the mobility of P to the mobility of Q?
  1. 3 : 1
  2. 3 : 4
  3. 2 : 3
  4. 4 : 3
Show answer
Answer: (D) 4 : 3
Explanation: Mobility is drift speed per unit field, μ = qτ/m. For P it is eτ/m. For Q it is 3e(τ/2)/(2m) = 3eτ/(4m). The ratio of P to Q is therefore 1 : 3/4 = 4 : 3.

Question 6

A copper wire of cross-section 1.0 mm² has 8.5 × 10²⁸ free electrons per m³ and carries a current of 3.4 A. At room temperature the free electrons have thermal speeds of about 1.2 × 10⁵ m/s. What is the approximate ratio of drift speed to thermal speed, and why does thermal motion alone give no current? (e = 1.6 × 10⁻¹⁹ C)
  1. About 5 × 10⁸; drift is so fast that it cancels the thermal motion
  2. About 2 × 10⁻⁹; thermal velocities are randomly directed and average to zero
  3. About 2 × 10⁻⁵; thermal velocities are randomly directed and average to zero
  4. About 2 × 10⁻⁹; electrons have no thermal motion between collisions with ions
Show answer
Answer: (B) About 2 × 10⁻⁹; thermal velocities are randomly directed and average to zero
Explanation: The drift speed is v = I/(neA) = 3.4/(8.5 × 10²⁸ × 1.6 × 10⁻¹⁹ × 1.0 × 10⁻⁶) = 2.5 × 10⁻⁴ m/s. Dividing by 1.2 × 10⁵ m/s gives about 2 × 10⁻⁹. The thermal speed is large, but its directions are random, so the average velocity and the net charge flow are zero. Only the very small drift superposed on this motion carries current.

Question 7

A metal block at absolute temperature T has no potential difference across it. Which statement correctly describes its free electrons?
  1. Their average velocity is proportional to T, which produces a small current
  2. They all move with the same velocity, and this does not depend on T
  3. Their average velocity is zero, but they keep moving randomly with a large thermal speed
  4. Each electron is at rest, so both the average velocity and the thermal speed are zero
Show answer
Answer: (C) Their average velocity is zero, but they keep moving randomly with a large thermal speed
Explanation: Free electrons move at high thermal speeds in random directions and collide with ions, and the rms thermal speed grows as √T. Because the directions are random, the velocities average to zero. So no net charge flows across any section and there is no current.
Doing well? Create a free account to take timed tests on this topic and see your weak areas.

Question 8

Three copper wires at the same temperature have these details. P: length L, diameter d, potential difference V. Q: length 2L, diameter 3d, potential difference 3V. R: length 3L, diameter 2d, potential difference V. What is the correct increasing order of the drift speed of electrons in them?
  1. Q < P < R
  2. R < P < Q
  3. P < R < Q
  4. R < Q < P
Show answer
Answer: (B) R < P < Q
Explanation: Drift speed is v = μE = μV/l for the same material, so it does not depend on the diameter. The fields are V/L for P, 1.5 V/L for Q and V/(3L) for R. The order of drift speed is therefore R < P < Q.

Question 9

Light balls with a conducting coating shuttle between two large parallel metal plates in vacuum, with gravity negligible. At each contact a ball acquires a charge proportional to the voltage between the plates, starts from rest, and crosses the gap in a uniform field; it does not rebound on arrival. If the voltage across the plates is tripled, the average current carried across the gap becomes
  1. 3 times
  2. 9 times
  3. 27 times
  4. √3 times
Show answer
Answer: (B) 9 times
Explanation: The charge on a ball is proportional to V and the field to V, so the force and acceleration are proportional to V². The crossing time, from h = ½at², therefore varies as 1/V. Average current is charge per crossing divided by crossing time, so it varies as V × V = V². Tripling the voltage makes the current 9 times.

Question 10

A constant potential difference is applied across a metal wire. It is then replaced by a wire of the same material with both its length and its diameter doubled, at the same temperature and with the same potential difference. Which description of the change is correct?
  1. Electric field stays the same, drift speed doubles, resistance doubles, current halves
  2. Electric field halves, drift speed halves, resistance halves, current doubles
  3. Electric field halves, drift speed halves, resistance doubles, current halves
  4. Electric field halves, drift speed stays the same, resistance halves, current doubles
Show answer
Answer: (B) Electric field halves, drift speed halves, resistance halves, current doubles
Explanation: With V fixed, E = V/L halves, and the drift speed eEτ/m halves with it. Resistance varies as L/D², so it changes by a factor of 2/4 = 1/2. The current V/R therefore doubles, which agrees with I = neAv_d, where the area is 4 times and the drift speed is half.

Question 11

A metal has 6.0 × 10²⁸ free electrons per m³ and resistivity 2.8 × 10⁻⁸ Ω m. If the electrons move with a mean speed of 1.6 × 10⁶ m/s between collisions, what is their mean free path? (m = 9.1 × 10⁻³¹ kg, e = 1.6 × 10⁻¹⁹ C)
  1. 1.7 × 10⁻⁸ m
  2. 3.4 × 10⁻⁸ m
  3. 3.4 × 10⁻⁹ m
  4. 6.8 × 10⁻⁷ m
Show answer
Answer: (B) 3.4 × 10⁻⁸ m
Explanation: Resistivity is ρ = m/(ne²τ), so τ = m/(ne²ρ) = 9.1 × 10⁻³¹/(6.0 × 10²⁸ × 2.56 × 10⁻³⁸ × 2.8 × 10⁻⁸) ≈ 2.1 × 10⁻¹⁴ s. The mean free path is the mean speed multiplied by the relaxation time. This gives 1.6 × 10⁶ × 2.1 × 10⁻¹⁴ ≈ 3.4 × 10⁻⁸ m.

Question 12

A wire of diameter 6.0 mm has a short necked section of the same material. A steady current flows through the wire, and the drift speed of the electrons in the neck is 2.25 times that in the main wire. What is the diameter of the neck?
  1. 2.7 mm
  2. 3.0 mm
  3. 4.0 mm
  4. 5.0 mm
Show answer
Answer: (C) 4.0 mm
Explanation: In steady flow the same current passes through both sections, and I = neAv_d with the same n. The drift speed is therefore inversely proportional to the area, that is, to the square of the diameter. The diameter ratio is √2.25 = 1.5, so the neck diameter is 6.0/1.5 = 4.0 mm.

Question 13

A metal conductor of uniform material narrows from a diameter of 4 mm to a diameter of 1 mm and carries a steady current. In the wide part the drift speed is 0.2 mm/s and the electric field is E. What are the drift speed and the electric field in the narrow part?
  1. 3.2 mm/s; E
  2. 3.2 mm/s; 16E
  3. 0.2 mm/s; 16E
  4. 0.8 mm/s; 4E
Show answer
Answer: (B) 3.2 mm/s; 16E
Explanation: The current is the same through every section, so current density J varies inversely as the area. Reducing the diameter to 1/4 reduces the area to 1/16, so J becomes 16 times larger. Since J = nev and J = E/ρ for the same material, both the drift speed and the field become 16 times larger.

Want more Electric Current, Drift Velocity and Mobility – Electric current questions?

E-GYAN NIDHI has 51 questions on this topic and 63,000+ in total, all free: timed CBT tests, NEET marking and instant analysis.

Register free Free Sunday Mock Test

More topics in CURRENT ELECTRICITY

↑