Question

A conductor of length $l$ is connected across an ideal cell of emf $E$.
Keeping the cell connected, the length of the conductor is increased to $2l$ by gradually stretching it.
If $R$ and $R'$ are the initial and final values of resistance, and $v_d$ and $v_d'$ are the initial and final values of drift velocity, find the relation between:
(i) $R'$ and $R$
(ii) $v_d'$ and $v_d$

Hint:

When a conductor is stretched, its length increases, causing the resistance to increase proportionally, while the drift velocity decreases due to the increased length.

Answer 1

% Option (i) When a conductor is stretched, its resistance changes because resistance is proportional to the length of the conductor. The resistance is given by: \[ R = \rho \frac{l}{A} \] where \( l \) is the length and \( A \) is the cross-sectional area. When the length is doubled, the resistance also doubles: \[ R' = 2R \] % Option (ii) The drift velocity is inversely proportional to the length of the conductor (as the potential difference and electric field remain the same): \[ v_d' = \frac{v_d}{2} \] Thus, the relations are: \[ R' = 2R \quad \text{and} \quad v_d' = \frac{v_d}{2} \] Thus, the final resistance is twice the initial resistance, and the final drift velocity is half the initial drift velocity.