COMEDK · Physics · 19. Current Electricity

Two cells with the same emf \(E\) and different internal resistances \(r_1\) and \(r_2\) are connected in series to an external resistance \(R\). If the potential difference across the first cell is zero then value of \(R\).

A \(\sqrt{r_1 r_2}\)
B \(r_1+r_2\)
C \(r_1-r_2\)
D \(\frac{r_1+r_2}{2}\)

Verified Solution

Answer & Solution

Correct Answer

(C) \(r_1-r_2\)

Step-by-step Solution

Detailed explanation

Here are two batteries with emf \(E\) each and the internal resistances \(r_1\) and \(r_2\), respectively. We have \(I\left(R+r_1+r_2\right)=2 E\) Now, the potential difference across the first cell would be equal to \(V=E-I r_1\). From the question, \(V=0\), there…

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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