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Class 12  »  Physics  »  Current Electricity

Electric Current and Drift Velocity - UNSOLVED PRACTICE SET

Class 12

Chapter: Current Electricity | Topic: Electric Current and Drift Velocity

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Class 12

ELECTRIC CURRENT AND DRIFT VELOCITY - UNSOLVED PRACTICE SET

Topic: Electric Current and Drift Velocity

Time: 49 mins | Marks: 30 | Difficulty: Medium

Multiple Choice Questions

Q1. Electric current is defined as:

  1. The rate of flow of charge per unit time 
  2. The total charge flowing through a conductor
  3. The potential difference across a conductor
  4. The resistance of a conductor

Q2. The SI unit of electric current is:

  1. Coulomb
  2. Ampere
  3. Volt
  4. Ohm

Q3. In a metallic conductor, electric current is due to the flow of:

  1. Protons
  2. Positive ions
  3. Free electrons
  4. Neutrons

Q4. The drift velocity of electrons in a conductor is typically of the order of:

  1. 10⁸ m/s
  2. 10⁶ m/s
  3. 10⁻⁴ m/s
  4. 10⁻¹ m/s

Q5. The relation between current I and drift velocity v_d is:

  1. I = n e A v_d
  2. I = n e v_d / A
  3. I = A v_d / n e
  4. I = n A / e v_d

Q6. If the cross-sectional area of a conductor is doubled while keeping the current constant, the drift velocity becomes:

  1. Doubled
  2. Halved
  3. Four times
  4. Unchanged

Short Answer Questions

Q7. Define electric current. Distinguish between conventional current and electron current.

Q8. What is drift velocity? Why is it much smaller than the random thermal velocity of electrons?

Q9. A copper wire of cross-sectional area 2 mm² carries a current of 4 A. If the number density of free electrons in copper is 8.5 × 10²⁸ m⁻³, calculate the drift velocity of electrons.

[Given: e = 1.6 × 10⁻¹⁹ C]

Q10. Why does the light in your room turn on instantly when you flip the switch, even though electron drift velocity is very small?

Q11. Write the expression relating current density J to drift velocity v_d. What is the SI unit of current density?

Q12. If the length of a conductor is doubled while keeping the same potential difference, what happens to the drift velocity? Explain.

Long Answer Questions

Q13. Derive the relation I = n e A v_d connecting electric current with drift velocity. Explain the physical meaning of each term in the equation.

Q14. Explain why the drift velocity of electrons in a conductor is very small (of the order of mm/s) even though the current flows almost instantaneously when a switch is turned on. Use the analogy of a water pipe to make your explanation clear.

Q15. A copper wire has length l = 2 m, cross-sectional area A = 1 mm², and carries a current I = 2 A. The number density of free electrons in copper is n = 8.5 × 10²⁸ m⁻³.

(a) Calculate the drift velocity of electrons.

(b) Calculate the time taken by an electron to travel the length of the wire.

(c) Compare this time with the time it takes for a bulb to glow after the switch is turned on. What conclusion can you draw?

[Given: e = 1.6 × 10⁻¹⁹ C]

Numerical / Application-Based Problems

Q16. In your school physics lab, a student measures the current through a copper wire of diameter 1 mm and finds it to be 5 A.

(a) Calculate the cross-sectional area of the wire.

(b) Find the drift velocity of electrons in the wire. [Given: n = 8.5 × 10²⁸ m⁻³ for copper]

(c) Calculate the current density in the wire.

(d) If the same current flows through an aluminium wire of the same diameter, will the drift velocity be the same or different? Explain. [Given: n_Al = 6.0 × 10²⁸ m⁻³]

[Given: e = 1.6 × 10⁻¹⁹ C]

Q17. A current of 10 A flows through a cylindrical copper wire of radius 0.5 mm.

(a) Calculate the drift velocity of electrons.

(b) How many electrons pass through a cross-section of the wire in 1 minute?

(c) If the wire is connected to a 12 V battery, and the electric field in the wire is uniform, calculate the time taken for an electron to drift from one end to the other if the wire is 3 m long.

(d) A student argues that since drift velocity is so small, electricity should take hours to reach our homes. Explain why this argument is wrong.

[Given: n = 8.5 × 10²⁸ m⁻³, e = 1.6 × 10⁻¹⁹ C]

Q18. Two wires A and B of the same material but different dimensions are connected in series across a battery. Wire A has length l and radius r, while wire B has length 2l and radius r/2.

(a) Compare the drift velocities of electrons in the two wires.

(b) Compare the current densities in the two wires.

(c) Compare the electric fields in the two wires if they have the same resistivity.

(d) If the current through the combination is 3 A, calculate the current through each wire and explain your answer.


Total: 30 Marks | Time: 49 mins

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