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Question

In the Fig. find I,R,ϵ1 and ϵ2

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A
8A,9Ω,54V,36V
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B
8A,9Ω,36V,54V
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C
9A,8Ω,36V,54V
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D
none of these
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Solution

The correct option is B 8A,9Ω,36V,54V
Redrawing and labeling the diagram as shown in figure.
Applying Kirchhoff's voltage law in loop ABFG,
2R+ϵ1ϵ2=0
2R+ϵ1=ϵ2...................(1)
Applying Kirchhoff's voltage law in loop BCDH
3(4)+I(3)ϵ1=0
3I+12=ϵ1...................(2)
Applying Kirchhoff's voltage law in loop ACEG
2R+3(4)5(6)=0
2R=3012
2R=18
R=9Ω......................(3)
Applying Kirchhoff's current at junction D
3+5=I
I=8A...................(4)
Using (4) in (2), we get
3(8)+12=ϵ1
ϵ1=36V..........................(5)
Using (5) and (3) in (1), we get
2(9)+36=ϵ2
ϵ2=54V........................(6)

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