Question

In a meter bridge experiment to determine the value of unknown resistance, first the resistances \(2\,\Omega\) and \(3\,\Omega\) are connected in the left and right gaps of the bridge and the null point is obtained at a distance \(l\) cm from the left end. Now, when an unknown resistance \(x\,\Omega\) is connected in parallel to \(3\,\Omega\), the null point is shifted by \(10\,\text{cm}\) to the right. The value of \(x\) is ________ \(\Omega\).

Hint:

Parallel combinations always reduce equivalent resistance.

Answer 1

Correct Answer: 6

Step 1: Write balance condition for meter bridge.
\[ \frac{2}{3} = \frac{l}{100 - l} \Rightarrow l = 40\,\text{cm} \]
Step 2: New null point position.
Shift is \(10\,\text{cm}\) to the right, so \[ l' = 50\,\text{cm} \]
Step 3: New resistance in right gap.
\[ R = \frac{3x}{3 + x} \]
Step 4: Apply balance condition again.
\[ \frac{2}{R} = \frac{50}{50} = 1 \Rightarrow R = 2 \]
Step 5: Solve for \(x\).
\[ \frac{3x}{3 + x} = 2 \Rightarrow 3x = 6 + 2x \Rightarrow x = 6 \]