Question

Two wires A and B of same material having length \(L_A, L_B\) and radii \(R_A, R_B\) and drift velocity \(V_A, V_B\) respectively carries same current. If \(L_A = L_B\) and \(R_A = 2 R_B\) then the value of \(\frac{V_A}{V_B}\) is

• A. 0.25
• B. 0.5
• C. 2.0
• D. 1.0

Hint:

Drift velocity is inversely proportional to the square of radius for same material and current.

Answer 1

The Correct Option is A

Current is: \[ I = n e A v_d = \text{constant} \Rightarrow v_d \propto \frac{1}{A} \Rightarrow \frac{V_A}{V_B} = \left( \frac{R_B}{R_A} \right)^2 = \left( \frac{1}{2} \right)^2 = 0.25 \]