A) \[\frac{10}{3}\Omega \]
B) \[\frac{20}{3}\Omega \]
C) \[\frac{16}{2}\Omega \]
D) none of these
Correct Answer: A
Solution :
The given figure represented balanced Wheat, stone bridge since, \[\frac{A}{B}=\frac{2\Omega }{3\Omega }=1.5\Omega ,\frac{C}{D}=\frac{6\Omega }{4\Omega }=1.5\Omega \] Hence, the potential between R and S same therefore resistance in the arm RS of \[7\Omega \] resistance is in effective. The resistance in the upper arm are connected in series combination. Hence the equivalent resistance of the upper arm is given by \[{{R}_{V}}=2+3=5\Omega \] Similarly the resistance in the lower arm are also connected in the series combination, hence their equivalent resistance is \[{{R}_{L}}=4+6=10\Omega \] Now\[{{R}_{U}}\]and\[{{R}_{L}}\]are in parallel combination. Therefore the equivalent resistance is \[{{\operatorname{R}}_{eq}}=\frac{5\times 10}{5+10}=\frac{50}{15}=\frac{10}{3}\Omega \]
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