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Q.
In the circuit shown below, the charge on the $60 \, μF$ capacitor is
NTA AbhyasNTA Abhyas 2020Electrostatic Potential and Capacitance
Solution:
The circuit shown in the figure is a balanced Wheatstone bridge, so the $80μF$ doesn't have any effect on the circuit and it can be removed.
After removing the $80μF$ , we see that the $30μF$ and $60μF$ are in series. Similarly, the $15μF$ and $30μF$ are also in series.
$C_{1}=\frac{30 \times 60}{30 + 60}=20μF$ , $C_{2}=\frac{15 \times 30}{15 + 30}=10μF$
Hence, the equivalent capacitance of the entire circuit is
$C=C_{1}+C_{2}=30μF$
$C_{eq}=\frac{C \times 30}{C + 30}=15μF$
The charge that flows through the battery = $10\times 15=150μC$
This charge will be divided into two branches in the ratio of capacitances.
On solving we get that charge on $60μF$ = $100μC$
