Question

A $4\mu \text{F}$ and a $9\mu \text{F}$ capacitors are connected in series combination across a $26\text{V}$ battery. What is the voltage (in $\text{V}$) of the battery required to charge the capacitors in parallel combination to the same total energy?

Answer 1

Equivalent capacitance in series combination is,

$C_1=\frac{9\times 4}{9+4}=\frac{36}{13}\mu \text{F}$

Also, equivalent capacitance in parallel combination is,

$C_2=9+4=13\mu \text{F}$

Given,

Total energy in series $=$ Total energy in parallel

$\Rightarrow \frac{1}{2}{C}_1{V}_1^2=\frac{1}{2}{C}_2{V}_2^2$

$\Rightarrow \frac{1}{2}\times \frac{36}{13}\times {26}^2=\frac{1}{2}\times 13\times V_2^2$

$\therefore V_2=12\text{V}$