First slide

Drift velocity

Question

Two ends of a cylindrical copper rod are connected to the terminals of a battery and the drift velocity of free electrons is found to be V. Now the copper rod is stretched to twice its original length and the ends of this deformed rod are connected to the terminals of the same battery. Then new drift velocity of free electrons in the rod will be

Moderate

Solution

If R be the original resistance of the rod,
$\begin{array}{l} T h e n V = \frac{i}{A n e} = \frac{ε}{R A n e} \\ R^{'} = n e w r e s i s t a n c e o f t h e r o d = ρ . \frac{l^{'}}{A^{'}} = ρ . \frac{2 l}{(A / 2)} = 4 (ρ \frac{l}{A}) = 4 R [∵ l^{'} A^{'} = l A] \\ V^{'} = \frac{ε}{(4 R) (\frac{A}{2}) n e} = \frac{V}{2} \end{array}$

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