First slide

Drift velocity

Question

Two ends of a metallic wire of length l and radius r are connected to the terminals of a battery of emf E and the drift velocity of free electrons is found to be ‘V’ . What will be the drift velocity of free electrons when the ends of a metallic wire made of same material having length 2l and radius 2r are connected to the terminals of a battery of emf 2E?

Moderate

A

2V
B

V/2
C

4V
D

V

Solution

$\begin{array}{l} V_{d} = \frac{j}{n e} = \frac{i}{A n e} = \frac{E}{RAn e} = \frac{E}{(ρ . \frac{l}{A}) An e} = \frac{E}{ρ n e l} \\ ∴ \frac{V^{1}}{V} = (\frac{E^{1}}{E}) (\frac{l}{l^{1}}) = (2) (\frac{1}{2}) = 1 \Rightarrow V^{1} = V \end{array}$

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