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Two cells of same emf E but internal resistance r1 and r2 are connected in series to an external resistor R (Fig.). What should be the value of R so that the potential difference across the terminals of the first cell becomes zero.

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\(I=\frac{E+E}{R+r_1+r_2}\)

V1 = E - Ir1 = E - \(\frac{2E}{r_1+r_2+R}r_1=0\)

or  \(E=\frac{2Er_1}{r_1+r_2+R}\)

\(\Rightarrow\) r1 + r2 + R = 2r1

\(\Rightarrow\) R = r1 - r2

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