Question

Effective capacitance of parallel combination of two capacitors $C_1$ and $C_2$ is $10\, \mu \,F$. When these capacitors are individually connected to a voltage source of $1 V$ , the energy stored in the capacitor $C_2$ is $4$ times that of $C_1$. If these capacitors are connected in series, their effective capacitance will be :

• A. 1.6 $\mu F$
• B. 8.4 $\mu$F
• C. 3.2 $\mu$F
• D. 4.2 $\mu$F

Answer 1

Answer: (A)

$C_{1}+C_{2}=10...\left(i\right)$
$\frac{1}{2}C_{2}V^{2}=4\times\frac{1}{2}C_{1}V^{2}$
$\therefore C_{2}=4C_{1}$
$\therefore C_{1}=2 \,\&\,C_{2}=8$
For series combination
$C_{eq}=\frac{C_{1}C_{2}}{C_{1}+C_{2}}=1.6$