First slide

Drift velocity

Question

When a potential difference is applied across a cylindrical wire, average drift speed of free electrons is ‘V’. Now the wire is stretched to two times its original length and same potential difference is applied across it. Then the new drift speed of free electrons will be ______

Moderate

Solution

Volume of wire remains constant.
$\begin{array}{l} ∴ a' l' = a l \Rightarrow a' = \frac{a l}{2 l} = \frac{a}{2} \\ R = I n i t i a l r e s i s t a n c e = ρ \frac{l}{a} \\ ∴ R^{'} = ρ . \frac{l'}{a'} = ρ . \frac{2 l}{\frac{a}{2}} = 4 R \\ N o w V_{d} = \frac{i}{a n e} = \frac{E}{R a n e} \\ ∴ \frac{{v_{d}}^{'}}{v_{d}} = \frac{R}{R^{'}} . \frac{a}{a^{'}} = \frac{1}{4} . 2 = \frac{1}{2} \\ ∴ {v^{'}}_{d} = \frac{1}{2} v_{d} = \frac{v}{2} \end{array}$

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