Question

Two wires A and B of equal lengths are connected in left and right gap respectively of a metre bridge, null point is obtained at 40 cm from left end. Diameters of the wires A and B are in the ratio 3:1 respectively, the ratio of specific resistance of A to that of B is

• A. \(2:1\)
• B. \(3:1\)
• C. \(6:1\)
• D. \(12:1\)

Hint:

Use the metre bridge balance condition, then write resistance in terms of resistivity, length and area.

Answer 1

The Correct Option is C

Step 1: Start with balance.
$R_A : R_B = 40 : 60 = 2 : 3$.

Step 2: Include geometry.
For equal lengths, $R \propto \rho/d^2$. So $\dfrac{\rho_A/9}{\rho_B/1} = \dfrac{2}{3}$.

Step 3: Solve.
$\dfrac{\rho_A}{\rho_B} = \dfrac{2}{3}\times 9 = 6$.

Final Answer:
Option (C). \[ \boxed{6 : 1} \]