Question

The given circuit shows a uniform straight wire AB of 40 cm length fixed at both ends. In order to get zero reading in the galvanometer G, the free end of J is to be placed from B at:

• A. 32 cm
• B. 8 cm
• C. 16 cm
• D. 24 cm

Answer 1

The Correct Option is D

For zero galvanometer deflection, the bridge must be balanced. This is a Wheatstone bridge arrangement.

The condition for a balanced Wheatstone bridge is:

$\frac{R_1}{R_2} = \frac{R_3}{R_4}$

Where R₁, R₂, R₃, and R₄ represent the resistance in each arm of the Wheatstone bridge. Here, R₁ and R₂ are the resistances of the wire segments AJ and JB respectively, and R₃ = 8 Ω and R₄ = 12 Ω.

The length of AB is 40 cm, thus, $\frac{R_1}{R_2} = \frac{8}{12} = \frac{2}{3}$

$\frac{R_1}{R_2} = \frac{x}{40 - x} = \frac{2}{3}$

3x = 80 − 2x 5x = 80 x = 16 cm

Distance of J from B = 40 cm − 16 cm = 24 cm