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Two cells with identical emf are connected to an external resistor R. Their internal resistances are R1 and R2, with R1 > R2. If the potential difference across the cell having internal resistance R2 becomes zero, then which relation for R is correct?

1. R = R2 - R1
2. R = R2(R1 + R2)/(R2 - R1)
3. R = R1R2/(R2 - R1)
4. R = R1R2/(R1 - R2)

Correct answer: R = R2 - R1

Solution

With both cells in series, current I = 2E/(R+R1+R2). The terminal PD across the cell of internal resistance R2 is E - I*R2 = 0, giving I = E/R2. Equating: R + R1 + R2 = 2*R2, so R = R2 - R1.

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