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Question

In the adjoining circuit diagram each resistance is of 10Ω. The current in the arm AD will be

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A
2i5
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B
3i5
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C
4i5
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D
i5
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Solution

The correct option is A 2i5
Let the current through arm AB, AD & BC are i1,i2 and i3 respectively.
Therefore current through BE & CF are i1i3 and i2+i3 respectively.
Let potential at A be V.
Using Kirchhoff's Law:
i=i1+i2
Therefore potential at C from both sides must be equal:
ViRi3R=V2i2R
ii+i3=2i2
Also at F potential from both side must be equal:
ViR(i1i3)2R=V2i2R
ViiR(iii3)2R=V2i2R(ii+i3)R
ii+(iii3)2=2i2+(ii+i3)3ii2i3=3i2+i3ii=i3+i2ii=2i2ii+i22ii=3i22i2i2=3i2i2=25i

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