Question

A capacitor with stored energy $4.0$ $J$ is connected with an identical capacitor with no electric field in between. Find the total energy stored in the two capacitors.

Answer 1

Let initial charge on the capacitor was $Q$ and capacitance is $C$

The energy stored in the capacitor is given as:

$E=\frac{Q^2}{2C}$

$\frac{1}{2}\frac{Q^2}{C}=4J$

As the new capacitor is connected, the net charge will be distributed between the capacitors.

Now, when two capacitors of same capacitance are present:

$\Rightarrow E^{\prime }=\frac{1}{2}\frac{Q^2}{4C}+\frac{1}{2}\frac{Q^2}{4C}$

$\Rightarrow E^{\prime }=\frac{1}{2}\frac{Q^2}{2C}$

$\Rightarrow E^{\prime }=2J$