A) \[10\Omega \]should be connected in parallel with A
B) \[10\Omega \] should be connected in series with A
C) \[5\Omega \]should be connected in series with B
D) \[5\Omega \] should be connected in parallel with B
Correct Answer: A
Solution :
Resistance in upper arms \[A=10\Omega ;B=5\Omega \] Resistance in lower arm \[C=4\Omega ;D=4\Omega \] The condition required to form a Wheatstone bridge is \[\frac{A}{B}=\frac{C}{D}\]which does not satisfy this case. If a \[10\Omega \] resistance is connected in parallel with A [as per option ] The relation for a new resistance is \[\frac{1}{A}=\frac{1}{10}+\frac{1}{10}+\frac{2}{10}=\frac{1}{5}\] \[A=5\Omega \] Now the network satisfies the condition of Wheatstone bridge \[\frac{P}{5}=\frac{R}{5}\]or\[\frac{5}{5}=\frac{4}{4}\]
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