Current Electricity 2 Question 21
21. For the resistance network shown in the figure, choose the correct option(s).
(2012)
(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) $I _2=2 A$
Integer Answer Type Questions
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Solution:
- Due to symmetry on upper side and lower side, points $P$ and $Q$ are at same potentials. Similarly, points $S$ and $T$ are at same potentials. Therefore, the simple circuit can be drawn as shown below
$$ \begin{aligned} I _2 & =\frac{12}{2+2+2}=2 A \\ I _3 & =\frac{12}{4+4+4}=1 A \\ \text { because } \quad I _1 & =I _2+I _3=3 A \\ I _{P Q} & =0 \\ V _P & =V _Q \end{aligned} $$
Potential drop (from left to right) across each resistance is
$$ \begin{aligned} \frac{12}{3} & =4 V \\ \therefore \quad V _{M S} & =2 \times 4=8 V \\ V _{N Q} & =1 \times 4=4 V \text { or } V _S<V _Q \end{aligned} $$
