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Kirchhoff's Voltage Law

In the circui...

Question

In the circuit, as shown in the figure, $ε = 5 V, r = 1 Ω, R_{2} = 4 Ω, R_{3} = 3 Ω$ and $C = 3 μ F$ . Find the charge on the plates of capacitor $A$ (in $μ C$ ) after achieving steady state.

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Solution

In steady state, there will be no current through the branches having capacitors.

So, current through resistor $R_{2}$ ,

$I_{2} = \frac{ϵ}{r + R_{2}} = \frac{5}{1 + 4} = 1 A$

Now, $V_{14} = I_{2} R_{2} = 1 \times 4 = 4 V$

Also, $V_{12} = V_{14} / 2 = 4 / 2 = 2 V$

$[$ As there is no current through $R_{1}]$

Further,

$Q = C V_{12} = 3 \times 2 = 6 μ C$

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