Question

In the network of capacitors shown in the diagram, the terminal A is at a potential of $20V$ and the terminal B is grounded. If $1F$ capacitor is charged to $10C$, then :

• A. the effective capacitance between A and B is $1.5F$.
• B. the potential drop across $2F$ capacitor is $20V$.
• C. each $3F$ capacitor is charged to $10C$.
• D. net charge leaked to ground is zero.

Answer 1

Answer: (A), (C)

The correct options are
A the effective capacitance between A and B is $1.5F$.
C each $3F$ capacitor is charged to $10C$.

Equivalent capacitance between AB is given by

$\frac{1}{C_{AB}}=\frac{1}{\frac{1}{\frac{1}{3}+\frac{1}{3}+\frac{1}{3}}+2}+\frac{1}{1+\frac{1}{\frac{1}{4}+\frac{1}{4}}}$

$\frac{1}{C_{AB}}=\frac{1}{3}+\frac{1}{3}=\frac{2}{3}$

Hence , equivalent capacitance $=1.5F$

Charge on 1F$=10C\Rightarrow V_c=V_D=\frac{10}{1}=10V$

Since$V_A=20V$, Potential drop across the $2F$ capacitor , $V_A-V_C=20-10=10V$

Equivalent capacitance of the three 3$F$ capacitances in series is $=\frac{1}{C}=\frac{1}{3}+\frac{1}{3}+\frac{1}{3}$

$\therefore C=1F$

$\therefore$ charge on each 3F$=10\times 1=10C$

Further, charge on +ve plate of $1.5F$ capacitor$=+30C$

$\therefore$ charge leaking to the ground (to make second plate $-30C$) is $+30C$