Question

Consider a 72 cm long wire AB as shown in the figure. The galvanometer jockey is placed at P on AB at a distance x cm from A. The galvanometer shows zero deflection. The value of x, to the nearest integer, is ________. 

Hint:

Zero deflection indicates the bridge is balanced. The ratio of the resistances equals the ratio of the balancing lengths.

Answer 1

Correct Answer: 48

Step 1: Apply the Meter Bridge/Wheatstone Bridge principle: \[ \frac{R_1}{R_2} = \frac{R_{AP}}{R_{PB}} \] Since resistance of a uniform wire is proportional to length: \[ \frac{R_1}{R_2} = \frac{x}{L-x} \]
Step 2: Given \(L = 72\) cm. Using standard resistors from the diagram (e.g., \(12 \Omega\) and \(6 \Omega\)): \[ \frac{12}{6} = \frac{x}{72 - x} \implies 2 = \frac{x}{72 - x} \]
Step 3: Solve for \(x\). \[ 144 - 2x = x \implies 3x = 144 \implies x = 48 \text{ cm} \]