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Question

Two ideal batteries of emf V1 and V2 and three resistances R1, R2 and R3 are connected as shown in the figure. The current in resistance R2 would be zero if
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A
V1=V2 and R1=R2=R3
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B
V1=V2 and R1=2R2=R3
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C
V1=2V2 and 2R1=2R2=R3
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D
2V1=V2 and 2R1=R2=R3
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Solution

The correct options are
A V1=V2 and R1=2R2=R3
B 2V1=V2 and 2R1=R2=R3
C V1=V2 and R1=R2=R3
Writing Kirchoff's laws for the top and bottom loops ,
V1i1R1(i1i2)R2=0
V2i2R3+(i1i2)R2=0
If Current through R2 is zero , i1=i2
Substituting in the above equations, we get:
V1V2=R1R3
Substituting the values given in the options and verifying,
options A , B and D satisfy this condition.

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