MHT CET · Physics · Current Electricity

In a meter bridge experiment, the balance point is obtained at length \(\ell_1 \mathrm{~cm}\) from left end when resistances in the left gap and right gap are \(5 \Omega\) and \(R \Omega\) respectively. When the resistance \(R\) is shunted with equal resistance, the new balance point is at \(1.6 \ell_1\). The resistance \(\mathrm{R}\) in ohm is

A 25
B 15
C 10
D 20

Verified Solution

Answer & Solution

Correct Answer

(B) 15

Step-by-step Solution

Detailed explanation

\(
\frac{5}{R}=\frac{\ell_1}{100-\ell_1}
\)
When \(\mathrm{R}\) is shunted,
\(
\begin{aligned}
& \frac{5 \times 2}{\mathrm{R}}=\frac{1.6 \ell_1}{100-1.6 \ell_1} \\
& \therefore \frac{5}{\mathrm{R}}=\frac{0.8 \ell_1}{100-1.6 \ell_1}
\end{aligned}
\)
Equating (1) and (2) and solving we get \(\ell_1=25 \mathrm{~cm}\) Putting this in Eq. (1), we get \(R=15 \Omega\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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