Question

We have a combination as shown in following figure. Choose the correct option(s)

• A. The charge on each capacitor is $600\mu \text{C}$
• B. The potential difference between the plates of $C_1$ is $30\text{V}$
• C. The potential difference between the plates of $C_2$ is $20\text{V}$
• D. The potential difference between the plates of $C_3$ is $40\text{V}$

Answer 1

Answer: (A), (B), (C), (D)

The potential difference between the plates of $C_3$ is $40\text{V}$


All capacitors are in series
$\frac{1}{C_{eq}}=\frac{1}{20}+\frac{1}{30}+\frac{1}{15}$
$\frac{1}{C_{eq}}=\frac{3+2+4}{60}=\frac{9}{60}$
$C_{eq}=\frac{60}{9}=\frac{20}{3}\mu \text{F}$
Applying $Q=CV$
$Q=\frac{20}{3}\times (90-0)$
$Q=600\mu \text{C}$
In series charge on each capacitor will be same, potential difference on each capacitor is
$\Rightarrow V_{C_1}=\frac{600}{20}=30\text{V}$
$\Rightarrow V_{C_2}=\frac{600}{30}=20\text{V}$
$\Rightarrow V_{C_3}=\frac{600}{15}=40\text{V}$