Question

In meter-bridge experiment a resistance of \(18\,\Omega\) is connected in left gap and unknown resistance \(R\) is connected in right gap. The null point is obtained at \(\ell_1\) from left end. If unknown resistance is replaced by \(\left(\frac{R}{3}\right)\Omega\), the null point is obtained at \(1.5\ell_1\). The unknown resistance is

• A. \(9\,\Omega\)
• B. \(36\,\Omega\)
• C. \(18\,\Omega\)
• D. \(27\,\Omega\)

Hint:

In meter bridge problems, use ratio form carefully for multiple balance conditions.

Answer 1

The Correct Option is C

Step 1: Balance condition for meter bridge.
\[ \frac{18}{R} = \frac{\ell_1}{100-\ell_1}. \]
Step 2: Second balance condition.
When resistance becomes \(R/3\), \[ \frac{18}{R/3} = \frac{1.5\ell_1}{100-1.5\ell_1}. \]
Step 3: Solving the equations.
From both equations, solving gives \[ R = 18\,\Omega. \]
Step 4: Conclusion.
The unknown resistance is \(18\,\Omega\).