Question

A network of four 20 $\mu F$ capacitors is connected to a 600 V supply as shown in the figure. The charge on capacitors $C_1$ and $C_4$ are

• A. $4\times {10}^{-3}C,12\times {10}^{-3}C$
• B. $6\times {10}^{-3}C,12\times {10}^{-3}C$
• C. $2\times {10}^{-3}C,4\times {10}^{-3}C$
• D. $3\times {10}^{-3}C,2\times {10}^{-3}C$

Answer 1

The correct option is A $4\times {10}^{-3}C,12\times {10}^{-3}C$

Charge on each capacitor, $C_1,C_2,C_3$ is same $=q$ Let charge on $C_4$ be $q^{\prime }$
$\frac{q}{C_1}+\frac{q}{C_2}+\frac{q}{C_3}=600$
or $q[\frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3}]=600$
or $\frac{q}{C_s}=600$
$\therefore q=600C_s=600\times \frac{20}{3}\mu C=4000\times {10}^{-6}C=4\times {10}^{-3}C$
Also $q^{\prime }=C_4\times 600\mu C=20\times 600\mu C=12\times {10}^{-3}C$