5.2 Energy stored in Capacitors

So the question is now then, How much energy is stored in the capacitors?

We know from the previous section that the charge stored in the capacitors is given by,$$Q=CV$$
where, $Q=$ charge stored in the capacitors, in coulombs($Q$)
           $V=$ potential difference between the plates, measured in volt($V$)
           $C=$ capacitance, measured in farad($F$)

Now, we can plot the Potential difference vs Charge  (i.e. $V$ vs $Q$) to check that its a straight line as follows,

Then, the energy stored in the capacitor is the work done to store the charge on the capacitor at the applied p.d. and is given by,$$E=\frac{1}{2}VQ=\frac{1}{2}CV^{2}$$
where, $Q=$ charge stored in the capacitors, in coulombs($Q$)
           $V=$ potential difference between the plates, measured in volt($V$)
           $E=$ Energy stored, in Joules($J$)

The above relation is given by finding the area under the curve. So, Energy in the ($V$ vs $Q$) graph is the quantity of area under the graph.


Here, a wonderful video of the energy stored in the capacitors. The reason for $\frac{1}{2}$ in the formula is also explained intuitively in the video, enjoy!!