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Question

In the circuit shown in figure, what will be the effective resistance between point A and B ?

1022129_034f28a6b97e4b9291b87634950b3005.png

A
r
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B
r2
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C
r3
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D
2r
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Solution

The correct option is B r2
The upper five resistance between A and B will form a balanced Wheatstone bridge hence there will be no current in the arm CO
the equilibrium circuit will be shown in fig.2
hence the resistance of arm ACB,AOB, and AB are all in parallel
the effective resistance between A and B is given as
1R=1(r+r)+1(r+r)+1r=12r+12r+1r=22r+1r=1r+1r1R=2rR=r2Ω

1127232_1022129_ans_d14cce592fb24edeb3962f200966b016.PNG

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