Question

Two capacitors of capacity $4\mu F$ and $6\mu F$ are connected in series and a battery is connected to the combination. The energy stored is $E_1$. If they are connected in parallel and if the same battery is connected to this combination, the energy is $E_2$ . The ratio $E_1:E_2$ is:

• A. $4:9$
• B. $9:14$
• C. $6:25$
• D. $7:12$

Answer 1

The correct option is C $6:25$

Let $V$ be voltage across the battery.

When the capacitors are in series, equivalent capacitance , $C_s=\frac{4\times 6}{4+6}=2.4\mu F$

When the capacitors are in parallel, equivalent capacitance , $C_p=4+6=10\mu F$

Now, $E_1=\frac{1}{2}{C}_s{V}^2$ and $E_2=\frac{1}{2}{C}_p{V}^2$

Thus, $\frac{E_1}{E_2}=\frac{C_s}{C_p}=\frac{2.4}{10}=\frac{6}{25}$