Question

Four capacitors and a battery are connected as shown in the figure. If the potential difference across the $7\mu F$ capacitor is $6V$, then which of the following statement(s) is/are correct?

• A. The potential drop across the $12\mu F$ capacitor is $10V$.
• B. The charge in the $3\mu F$ capacitor is $42\mu C$.
• C. The potential drop across the $3\mu F$ capacitor is $10V$.
• D. The emf of the battery is $30V$.

Answer 1

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

The correct options are
A The potential drop across the $12\mu F$ capacitor is $10V$.
B The charge in the $3\mu F$ capacitor is $42\mu C$.
D The emf of the battery is $30V$.



Potential across $7\mu F$ capacitor $=6V$
Potential across the $3\mu F$ capacitor $=\frac{7}{3}\times 6=14V$

Therefore, the potential across the combination of $7\mu F$ and $3\mu F$ capacitor is $14+6=20V$

Which means the potential across the combination of $7\mu F$, $3\mu F$ and $3.9\mu F$ (equivalent $6\mu F$) is also $20V$

Therefore,
Potential across the $12\mu F$ capacitor $=\frac{20}{2}=10V$. (a) is correct.

Charge on $3\mu F$ capacitor $=14\times 3=42\mu C$. (b) is correct.

Potential across the $3\mu F$ capacitor $=14V$. So (c) is wrong.

Emf of the cell $=20+10=30V$