A) \[8\,\Omega \]
B) \[2.4\,\Omega \]
C) \[4.5\,\Omega \]
D) \[3\,\Omega \]
Correct Answer: B
Solution :
The arms PR, RQ, SP, QS satisfy the condition to from a balanced Wheatstone bridge i.e., \[\left[ \frac{P}{Q}=\frac{R}{S}=\frac{1}{2}=\frac{4}{8} \right]\] Hence, the points R and S are at same potential and resistance RS of\[3\,\Omega \]is not to be taken into consideration. Resistances of upper arm which are connected in series combination their equivalent resistance is given by \[{{R}_{U}}=1+2=3\,\Omega \] Similarly resistances of lower arm which are also connected in series their equivalent resistance is \[{{R}_{L}}=4+8=12\,\Omega \] The resistances\[{{R}_{U}}\] and\[{{R}_{L}}\]are connected in parallel combination then their equivalent resistance between P and Q is \[\frac{1}{{{R}_{PQ}}}=\frac{1}{3}+\frac{1}{12}=\frac{5}{12}\] Or \[{{R}_{PQ}}=\frac{12}{5}=2.4\,\Omega \]
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