Drift Velocity MCQs with Solutions

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Drift velocity is defined as the average velocity attained by the electrons moving inside a conductor in the presence of an external electric field. The applied electric field is the force responsible for pushing electrons towards the higher potential. Drift velocity is an important concept of chapter Current Electricity.

When an electric field is applied, electrons undergo collisions with the heavy ions inside the conductor and hence move in random directions. The time interval between two successive collisions of electrons is called relaxation time.

The drift velocity of a moving electron is given by;

v_d = I / neA

where;

v_d = drift velocity

I = current flow

n = free electron density

e = charge of an electron

A = cross-sectional area

Check Also: NCERT Solutions for Class 12 Physics Current Electricity

MCQs on Drift Velocity

Ques 1. The electric field E, current density J and conductivity of a conductor are related as:

\(\sigma\) = E/J
\(\sigma\) = J/E
\(\sigma\) = JE
\(\sigma\) = 1/JE

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Ans. (b). \(\sigma\) = J/E

Explanation: I = V/R

and R = p(L/a)

So, I = V / p(L/a)

I / A = V / pL

But we know that, I / A = J and V / L = E

Hence, J = \(\sigma\)E

\(\sigma\) = J/E

Ques 2. Two wires each of radius of cross-section r but of different materials are connected together end to end (in series). If the densities of charge carriers in the two wires are in the ratio 1:4, the drift velocity of electrons in the two wires will be in the ratio:

1:2
4:1
2:1
1:4

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Ans. (b). 4:1

Explanation: Let n₁ and n₂ be the densities of charge carriers in the two wires. V_d1 and V_d2 are the drift velocities of the charge carriers, respectively.

I = n₁eAV_d1 = n₂eAV_d2

∴ n₁V_d1 = n₂V_d2

V_d1/V_d2 = n₂/n₁

V_d1/V_d2 = 4/1

Ques 3. A current of 5 A is passing through a metallic wire of cross-sectional area 4 x 10^-6 m². If the density of charge carriers of the wire is 5 x 10²⁶ m^-3, then the drift velocity of the electrons will be:

1 x 10² m/s
1.56 x 10^-2 m/s
1.56 x 10^-3 m/s
1 x 10^-2 m/s

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Ans. (b). 1.56 x 10^-2 m/s

Explanation: Drift velocity, v_d = I / nAe

v_d = 5 / (4 x 10^-6) (5 x 10²⁶) (1.6 x 10^-19)

v_d = 1.56 x 10^-2m/s

Ques 4. A current of 16 A is passed through a conductor with an electron density of 4 x 10²⁸ m^-3 and area of cross-section 10^-5 m². The average drift velocity of free electrons in the conductor is:

2.5 x 10^-4 m/s
6.4 x 10^-4 m/s
1.6 x 10^-4 m/s
3.2 x 10^-4 m/s

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Ans. (a). 2.5 x 10^-4 m/s

Explanation: In a small interval of time, dt, the number of electrons that leave a cross-section is

= (4 x 10²⁸)(10^-5) vdt

Charge crossing in time dt is,

dq = (1.6 x 10^-19)(4 x 10²⁸)(10^-5) vdt

I = dq/dt

I = 6.4 x 10⁴ v

16 = 6.4 x 10⁴ v

v = 2.5 x 10^-4 m/s

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Ques 5. Estimate the average drift speed of conduction electrons in a copper wire of cross-sectional area 1 x 10^-7 m² carrying a current of 1.5 A. Assume that each copper atom contributes roughly one conduction electron. The density of copper is 9 x 10³ kgm^-3 and its atomic mass is 63.5 amu.

3.1 x 10³ m/s
1.1 x 10^-3 m/s
4.1 x 10³ m/s
2.1 x 10³ m/s

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Ans. (b). 1.1 x 10^-3 m/s

Explanation: Molar mass of copper (M) = 63.5 g = 63.5 x 10^-3 kg

Density of copper (p) = 9 x 10³ kg/m³

No. of copper atoms per unit volume is,

N = no. of moles in unit volume no. of atoms in 1 mole (N_A)

No. of moles in unit volume = Mass of unit volume / mass of one mole

= Density / Molar mass = / M

Therefore,

N = ( p / M) x N_A

Where, N_A = 6.023 x 10²³

N = 9 x 10³ x 6.023 x 10²³ / 63.5 x 10^-3

N = 8.54 x 10²⁸ m^-3

Since one copper atom contributes one conduction electron. So, the number of conduction electron per unit volume = no. of copper atoms per unit volume

n = N = 8.54 x 10²⁸ m^-3

Now, drift velocity, Vd = I / neA

V_d = 1.5 / (8.5 x 10²⁸) x (1.6 x 10^-19) x (10^-7)

V_d = 1.1 x 10^-3 m/s

Ques 6. A current passes through a resistor. If K₁ and K₂ represent the average kinetic energy of the conduction electrons and the metal ions respectively then:

K₁ < K₂
K₁ = K₂
K₁ > K₂
Any of the above may occur

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Ans. (c). K₁ > K₂

Explanation: As per the law of conservation of momentum, electrons possess drift velocity greater than velocity of ions. Therefore, K₁ > K₂.

Ques 7. Drift velocity varies with the intensity of electric field as per the relation:

V_d ∝ E
V_d ∝ 1/E
V_d = constant
V_d ∝ E²

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Ans. (a). V_d ∝ E

Explanation: I = neAV_d

J = I/A

J = neV_d

Also, \(\sigma\)J = E

Therefore, neV_d = \(\sigma\)E

Hence, V_d ∝ E

Ques 8. Assertion: A current flows in a conductor only when there is an electric field within the conductor.

Reason: The drift velocity of electrons in the presence of electric fields decreases.

Both assertion and reason are true and reason is the correct explanation of the assertion
Both assertion and reason are true but reason is not the correct explanation of assertion
Assertion is true but reason is false
Assertion is false but reason is true

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Ans. (c). Assertion is true but reason is false

Explanation: Current flows when potential difference is present at the two ends of a conductor. Potential differences arise when an electric field is applied.

And drift velocity of electrons is directly proportional to the electric field.

Ques 9. Drift velocity depends upon the electric field, in which of the following dependence of drift velocity on the electric field ohm’s law is obeyed?

V_d ∝ E²
V_d ∝ E
V_d ∝ E^1/2
V_d = constant

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Ans. (b). V_d ∝ E

Explanation: Drift velocity, |v_d | = eE\(\tau\)/m

∴ V_d ∝ E

Ques 10. What is the effect of heating of a conductor on the drift velocity of free electrons?

Increases
Decreases
Remains constant
None of the above

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Ans. (b). Decreases

Explanation: When the conductor is heated, collisions between the electrons increases. As a result, relaxation time decreases and thus drift velocity also decreases.

V_d = (eE/m)\(\tau\)

Ques 11. A steady current flows in a metallic conductor of non-uniform cross-section. Which of the following quantities is constant along the conductor?

Drift Speed
Current
Current Density
None of these

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Ans. (b). Current

Explanation: V_d = I / enA or V_d ∝ 1/A

E = I/\(\sigma\)A or E ∝ 1/A

So, both V_d and E will change with A but current (I) will remain constant.

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Drift Velocity MCQs with Solutions

MCQs on Drift Velocity

CBSE CLASS XII Related Questions

1.
The resistance of a metal wire at \( 20^\circ \text{C} \) is \( 1.05 \, \Omega \) and at \( 100^\circ \text{C} \) is \( 1.38 \, \Omega \). Determine the temperature coefficient of resistivity of this metal.

2.
A student sets up the circuit as shown in the figure to find the value of unknown resistance X and records a set of readings of the voltmeter and the ammeter by using the rheostat.

4.
With the help of a labelled diagram, explain the principle, construction and working of an a.c. generator.

5.
Consider the nuclear reaction \( X \to Y + Z \). Let \( M_x \), \( M_y \), and \( M_z \) be the masses of the three nuclei X, Y, and Z respectively. Then which of the following relations hold true?

6.
Two metal spheres of radii $r_1$ and $r_2$ ($> r_1$) having charges $q_1$ and $q_2$ respectively kept in air, are brought in contact. Which of the following statements is not correct ?

Similar Physics Concepts

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Drift Velocity MCQs with Solutions

MCQs on Drift Velocity

CBSE CLASS XII Related Questions

1. The resistance of a metal wire at \( 20^\circ \text{C} \) is \( 1.05 \, \Omega \) and at \( 100^\circ \text{C} \) is \( 1.38 \, \Omega \). Determine the temperature coefficient of resistivity of this metal.

2.A student sets up the circuit as shown in the figure to find the value of unknown resistance X and records a set of readings of the voltmeter and the ammeter by using the rheostat.

4.With the help of a labelled diagram, explain the principle, construction and working of an a.c. generator.

5.Consider the nuclear reaction \( X \to Y + Z \). Let \( M_x \), \( M_y \), and \( M_z \) be the masses of the three nuclei X, Y, and Z respectively. Then which of the following relations hold true?

6.Two metal spheres of radii $r_1$ and $r_2$ ($> r_1$) having charges $q_1$ and $q_2$ respectively kept in air, are brought in contact. Which of the following statements is not correct ?

Similar Physics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
The resistance of a metal wire at \( 20^\circ \text{C} \) is \( 1.05 \, \Omega \) and at \( 100^\circ \text{C} \) is \( 1.38 \, \Omega \). Determine the temperature coefficient of resistivity of this metal.

2.
A student sets up the circuit as shown in the figure to find the value of unknown resistance X and records a set of readings of the voltmeter and the ammeter by using the rheostat.

4.
With the help of a labelled diagram, explain the principle, construction and working of an a.c. generator.

5.
Consider the nuclear reaction \( X \to Y + Z \). Let \( M_x \), \( M_y \), and \( M_z \) be the masses of the three nuclei X, Y, and Z respectively. Then which of the following relations hold true?

6.
Two metal spheres of radii $r_1$ and $r_2$ ($> r_1$) having charges $q_1$ and $q_2$ respectively kept in air, are brought in contact. Which of the following statements is not correct ?