Two cells of same emf E but internal resistance r1 and r2
Question:

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

Solution:

Effective emf of two cells = E + E = 2E

Effective resistance = R + r1 + r2

Electric current is given as

I = 2E/R+r1+r2

Potential difference is given as

V1 – E – Ir1 = 0

Which f=gives R = r1 – r2

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