Question

Four capacitors and a battery are connected as shown in 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 $30V$

Equivalent capacitance of network is $C_{eq}=4\mu F$.
Charge $Q=C_{eq}V=4V\mu C$
The charge on the $7\mu F$ or $3\mu F$ capacitor is
$Q_2=\left(7\mu F\right)\left(6V\right)=42\mu C$
$\frac{Q_2}{2.1\mu F}=\frac{Q_1}{12\mu F}or{Q}_1=\left(42\mu C\right)\frac{\left(3.9\mu F\right)}{\left(2.1\mu F\right)}=78\mu C$
$Q=Q_1+Q_2=(78\mu C+42\mu C)=120\mu C=4V\mu C$
Emf of the battery is $V=30V$
The potential drop across $12\mu F$ capacitor is
$\frac{Q}{12\mu F}=\frac{120\mu C}{12\mu F}=10V$