Question

A resistance is to be measured using a meter bridge; the student chooses the standard resistance R to be \(100\ \Omega\). The student finds the null point at \(l_{1}=16\) cm. To get the null point near the middle of the wire, the value of R will be

• A. \(49\ \Omega\)
• B. \(39\ \Omega\)
• C. \(19\ \Omega\)
• D. \(29\ \Omega\)

Hint:

First find the unknown resistance from the first balance point. For a middle null, the standard resistance should be close to it.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
Balance condition: \(\dfrac{X}{R}=\dfrac{l_{1}}{100-l_{1}}\).

Step 2: Find the unknown
\(X=100\times\dfrac{16}{84}\approx19\ \Omega\)

Step 3: Middle null point
The null is at 50 cm when both gap resistances are equal, so \(R\approx X\approx19\ \Omega\).

Final Answer:
The standard resistance should be about 19 ohm. \[ \boxed{\text{(C) }19\ \Omega} \]