COMEDK · Physics · 19. Current Electricity

An unknown resistance \(R_{1}\) is connected in series with a resistance of \(10 ~\Omega\). This combination is connected to one gap of a meter bridge, while a resistance \(R_{2}\) is connected in the other gap. The balance point is at \(50 \mathrm{~cm}\). Now, when the \(10 ~\Omega\) resistance is removed, the balance point shifts to \(40 \mathrm{~cm}\). The value of \(R_{1}\) (in \(\Omega\) ) is

A \(20\)
B \(10\)
C \(60\)
D \(40\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(20\)

Step-by-step Solution

Detailed explanation

In first case, \(P=R_{1}+10, Q=R_{2}, l=50 \mathrm{~cm}\) For balanced condition, \(\frac{P}{Q}=\frac{l}{100-l}\) \(\Rightarrow \quad \frac{R_{1}+10}{R_{2}}=\frac{50}{50}\) \(\Rightarrow \quad R_{1}+10=R_{2}\) Similarly, for second case, \(P=R_{1}, Q=R_{2}, l=40 \mathrm{~cm}\)…

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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