Shown in the figure is network of capacitors and resistors. The potentials of some of the nodes are given, Find the
(a) potential of $P$
(b) energy stored in the capacitor connected between R and S
(c) energy stored in the capacitor connected between P and Q

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Solution

At steady state, capacitor offers infinite resistance to DC, therefore, no current passes through $1 μ F$ capacitor and current passes through $1 Ω$ resistor across PQ. Since three identical resistors of resistance $\frac{1}{3} Ω$ each are connected in series. This series combination is connected in parallel with another resistor of $1 Ω$ across PQ
The effective resistance between P and Q will be $\frac{1}{2} Ω$
Applying KCL at P we obtain
$i_{1} + i_{2} + i_{3} = 0 \Rightarrow \frac{V_{p} - 10}{1} + \frac{V_{p} - 3}{0.3} + \frac{V_{p} - (- 20)}{1} = 0 \Rightarrow V_{p} [1 + \frac{1}{0.3} + 1] = 10 + 10 - 20$
(b) $V_{p} = 0; i_{1} = 10 a m p; i_{2} = - 10 a m p, i_{3} = 20 a m p$
The potential difference across PQ
$V_{P Q} = R_{P Q} . i_{3} \Rightarrow V_{P Q} = (1 / 2) 20 = 10 V$
Since $V_{p} = 0, V_{Q} = 0 - 10 V$
ie., $V_{P Q} = + 10 V$
The potential difference between R and S $= V_{R S}$
Since $i_{P R} = I_{P Q} / 2 = i_{3} / 2 = \frac{20}{10} = 10; V_{S} = 0; V_{P} = 0$
$V_{R} = V_{P} - (I_{P R}) (R_{P R}) = - [10 \times 1 / 3] = - \frac{10}{3} V$
(b) the energy stored in the capacitor $(0.4 μ F)$
$= \frac{1}{6} (0.4 \times 10^{- 6}) {(\frac{10}{3})}^{2} = 2.2 \times 10^{- 6} J$
(c) the Energy stored in the capacitor $(1 μ F)$
$= \frac{1}{2} (1 \times 10^{- 6}) 10^{2} = 50 μ J$

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Shown in the figure is network of capacitors and resistors. The potentials of some of the nodes are given, Find the(a) potential of P(b) energy stored in the capacitor connected between R and S(c) energy stored in the capacitor connected between P and Q

Shown in the figure is network of capacitors and resistors. The potentials of some of the nodes are given, Find the
(a) potential of $P$
(b) energy stored in the capacitor connected between R and S
(c) energy stored in the capacitor connected between P and Q