For the resistance network shown in the figure, choose the correct option$(s)$. $Image$

$(A)$ The current through $P Q$ is zero.

$(B)$ $I_1=3 A$.

$(C)$ The potential at $S$ is less than that at $Q$.

$(D)$ $I _2=2 A$.

Question

For the resistance network shown in the figure, choose the correct option$(s)$. $Image$

$(A)$ The current through $P Q$ is zero.

$(B)$ $I_1=3 A$.

$(C)$ The potential at $S$ is less than that at $Q$.

$(D)$ $I _2=2 A$.

IIT 2012, Diffcult

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Solution

Due to input and output symmetry $P$ and $Q$ and $S$ and $T$ have same potential. $Image$

$R_{e q}=\frac{6 \times 12}{18}=4 \Omega $

$I_1=\frac{12}{4}=3 A $

$I_2=\left(\frac{12}{6+12}\right) \times 3 $

$I _2=2 A $

$V _4- V _3=2 \times 4=8 V $

$V_A-V_T^3=1 \times 8=8 V $

$V_P=V_Q^{\top} \Rightarrow \text { Current through } P Q=0 $

$V_P=V_Q \Rightarrow V_Q>V_a $

$I_1=3 A $

$I _2=2 A $

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