MHT CET · Physics · Current Electricity

When a resistance of \(100 \Omega\) is connected in series with a galvanometer of resistance \(R\), its range is
V. To double its range, a resistance of \(1000 \Omega\) is connected in series. Find \(R\).

A \(700 \Omega\)
B \(800 \Omega\)
C \(900 \Omega\)
D \(100 \Omega\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(900 \Omega\)

Step-by-step Solution

Detailed explanation

When a resistance of \(100 \Omega\) is connected in series
\(
\text { current, } i=\frac{V}{100+R}
\)
when a resistance of \(1000 \Omega\) is connected in
series, the its range double
\(
\text { current, } i=\frac{2 V}{1100+R}
\)
From Eqs. (i) and (ii)
\(
\begin{aligned}
\frac{V}{100+R} &=\frac{2 V}{1100+R} \\
R &=900 \Omega
\end{aligned}
\)

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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When a resistance of \(100 \Omega\) is connected in series with a galvanometer of resistance \(R\), its range isV. To double its range, a resistance of \(1000 \Omega\) is connected in series. Find \(R\).

Step-by-step Solution

When a resistance of \(100 \Omega\) is connected in series with a galvanometer of resistance \(R\), its range is
V. To double its range, a resistance of \(1000 \Omega\) is connected in series. Find \(R\).