Question

A potential difference 'V' is applied across a conducting wire of diameter 'd' and length 'L'. When the diameter is doubled, the drift velocity-

1. becomes (1/4)^th of the initial value
2. decreases by three times
3. increases by four times
4. remains the same

Answer 1

Correct Answer - Option 1 : becomes (1/4)^th of the initial value

The correct answer is option 1) i.e. becomes (1/4)th of the initial value

CONCEPT:

• Drift velocity: The average velocity attained by the electrons under the influence of an electric field is termed the drift velocity. 
  • The free electrons are always in a constant random motion in the conductor.
  • When the conductor is connected to a battery, an electric field is generated.
  • When these free electrons are subjected to an electric field, they slowly drift in the direction of the electric field applied, while maintaining the random motion.
  • At this point, the net velocity of the electrons is called its drift velocity.

The drift velocity (vd) of the electron in a conductor is given by:

\(v_d =\frac{I}{nAq}\)

Where I is the current flowing through the conductor, A is the area of cross-section of the conductor, q is the charge on the electron and n is the number of electrons.

EXPLANATION:

We know that, \(v_d =\frac{I}{nAq}\)

A = πd²/4

So v_d ∝ 1/d²

• If the diameter is doubled then the drift velocity becomes (1/4)^th of the initial value.