Question

In the circuit, as shown in the figure, $\epsilon =5\text{V},r=1\Omega ,R_2=4\Omega ,R_3=3\Omega$ and $C=3\mu \text{F}$. Find the charge on the plates of capacitor $A$ (in $\mu C$) after achieving steady state.

Answer 1

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

So, current through resistor $R_2$,

$I_2=\frac{ϵ}{r+R_2}=\frac{5}{1+4}=1\text{A}$

Now, $V_{14}=I_2{R}_2=1\times 4=4\text{V}$

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

$[$As there is no current through $R_1]$

Further,

$Q=C{V}_{12}=3\times 2=6\mu \text{C}$