Question

In metre-bridge experiment the balance point is obtained if the gaps are closed by \(2 \Omega\) and \(3 \Omega\). A shunt of \(x \Omega\) is added to \(3 \Omega\) resistor to shift the balance point by \(22.5 \text{ cm}\). The value of \(x\) is.

• A. \(3\)
• B. \(2\)
• C. \(1\)
• D. \(4\)

Hint:

Shunting a resistor always decreases the total resistance in that gap, moving the balance point away from it.

Answer 1

The Correct Option is B

Step 1: Initial Balance
\(\frac{2}{3} = \frac{l}{100-l} \implies 200 - 2l = 3l \implies l = 40 \text{ cm}\).

Step 2: New Condition
Adding a shunt to the \(3 \Omega\) resistor (Right gap) decreases the resistance, shifting the balance point to the right.
New \(l' = 40 + 22.5 = 62.5 \text{ cm}\).

Step 3: Calculate Shunted Resistance
\(\frac{2}{R_p} = \frac{62.5}{37.5} = \frac{5}{3} \implies R_p = \frac{6}{5} = 1.2 \Omega\).

Step 4: Solve for x
\(\frac{1}{1.2} = \frac{1}{3} + \frac{1}{x} \implies \frac{1}{x} = \frac{1}{1.2} - \frac{1}{3} = \frac{5}{6} - \frac{2}{6} = \frac{3}{6} = \frac{1}{2}\).
\(x = 2 \Omega\).
Final Answer: (B)