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!!
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!!
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