Question

The diagram shows three capacitor with their capacitances with breakdown voltages. what should be the maximum value of external emf of source such that no capacitor breaks down :-

• A. $\frac{33}{2}$volt
• B. $\frac{11}{3}$volt
• C. $\frac{13}{3}$volt
• D. $\frac{11}{2}$volt

Answer 1

The correct option is B $\frac{11}{3}$volt

Maximum charge on $1\mu F$, $Q_1=CV=1\times 2=2\mu C$

Maximum charge on $2\mu F$, $Q_2=CV=2\times 1=2\mu C$

Maximum charge on $3\mu F$, $Q_3=CV=3\times 3=9\mu C$

So, maximum charge on the system is $Q=2\mu C$

Equivalent capacitance $\frac{1}{C_{eq}}=\frac{1}{C_1}+\frac{1}{C_2}+\frac{1}{C_3}$

So, $\frac{1}{C_{eq}}=\frac{1}{1}+\frac{1}{2}+\frac{1}{3}$

$⟹C_{eq}=\frac{6}{11}\mu F$

External emf $V=\frac{Q}{C_{eq}}=\frac{2}{6/11}=\frac{11}{3}$ volt