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Question

The emf (V) and internal resistance (r) of a single battery which is equivalent to a parallel combination of two batteries of emf's V1 and V2 and internal resistance r1 and r2, respectively, with polarities as shown in the figure are given by V1r2V2r1r1+r2,r1r2r1+r2.
1016648_3d6c27d8816e4816a5cf12492c6cb03a.PNG

A
True
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B
False
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Solution

The correct option is A True

The equivalent resistance, req=r1r2r1+r2

This is the internal resistance of the single battery which is
equivalent to a parallel combination of the two batteries
. Now
applying Kirchhoff s law in loop HCDEFGH moving clockwise
starting from D

Ir2+V2+V1Ir1=0

I=V1+V2r1+r2

VA+Ir1V1=VB

VAVB=V1Ir1

VAVB=V1(V1+V2)r1r1+r2=V1r1+V1r2V1r1V2r1r1+r2

VAVB=V1r2V2r1ri+r2

Hence, it is true


1053935_1016648_ans_a95a22b421a9401c863c810bdcd7f3fe.png

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