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Question

Two cells, having the same emf are connected in series through an external resistance R. Cells have internal resistance r1 and r2(r1>r2) respectively. When the circuit is closed, the potential difference across the first cell is zero, The value of R is

A
r1+r2
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B
r1r2
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C
r1+r22
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D
r1r22
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Solution

The correct option is B r1r2
Current inn the circuit is given by Ohm's law.
Net resistance of the circuit=R1+R2+R
Net emf in series=E+E=2E
Therefore, from Ohm's law, current in the circuit,
I=Netemfnetresistance
impliesI=2Er1+r2+R(1)
It is given that as circuit is closed, potential difference across the first cell is zero.
V=EIr1=0
I=Er1(2)
Equating (1) and (2)
Er1=2Er1+r2+R
2r1=r1+r2+R
External Resistance=R=r1r2

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