Question

A circuit has a section A B shown in the figure. The emf of the source equals $E=10V$, the capacitance of the capacitors $C_1$ is $1.0$ $\mu F$ and $C_2$ is $2.0$ $\mu F$ respectively and potential difference $V_A-V_B=$ $5V$. Then,

• A. potential difference across $C_1$ and $C_2$ are same.
• B. magnitude of Charge on $C_1$ is greater than magnitude of charge on capacitor $C_2$.
• C. potential difference across $C_{1}is\frac{10}{3}$ V and across $C_2$ is $\frac{5}{3}V$.
• D. potential difference across $C_{1}is\frac{5}{3}$ V and across $C_2$ is $\frac{10}{3}V$.

Answer 1

The correct option is C potential difference across $C_{1}is\frac{10}{3}$ V and across $C_2$ is $\frac{5}{3}V$.

See the diagram. Let charge on each capacitor is q then
$V_b+q/\left(2\mu F\right)+10V+q/\left(1\mu F\right)=V_a$
$\Rightarrow 3q/\left(2\mu F\right)=-5V\Rightarrow q=-10/3\mu C$
$V_{1\mu F}=10/3V$
$V_{2\mu F}=5/3V$