MHT CET · Physics · Current Electricity

Two known resistances are connected in two gaps of a meter bridge. The null point is obtained at \(20 \mathrm{~cm}\) from zero end. A resistance of \(15 \Omega\) is connected in series with the smaller of the two. The null point shifts to \(40 \mathrm{~cm}\). The smaller resistances is

A \(9 \Omega\)
B \(7 \Omega\)
C \(3 \Omega\)
D \(5 \Omega\)

Verified Solution

Answer & Solution

Correct Answer

(A) \(9 \Omega\)

Step-by-step Solution

Detailed explanation

Given \(l=20 \mathrm{~cm} \quad l^{\prime}=40 \mathrm{~cm}\)
Using \(\frac{R_1}{R_2}=\frac{l}{100-l}\)
\(\begin{aligned} & \therefore \frac{R_1}{R_2}=\frac{20}{100-20} \\ & \Rightarrow R_2=4 R_1\end{aligned}\)
Again using \(\frac{R_1}{R_2}=\frac{l^{\prime}}{100-l^{\prime}}\), where \(l^{\prime}=40 \mathrm{~cm}, R_1=R^{\prime}{ }_1+15\) and
\(\begin{aligned} & R_2^{\prime}=R_2=4 R_1 \\ & \therefore \frac{R_1+15}{4 R_1}=\frac{40}{100-40} \\ & \Rightarrow R_1=9 \Omega\end{aligned}\)

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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