Question

Deri ve an expression for energy stored in a capacitor ?

Answer 1

Step-by-step explanation:

Answer:

$U=\frac{1}{2}CV^2\;$

'or'

$\;U=\frac{1}{2}\frac{q^2}{C}$

Explanation:

Let that capacitance of a capacitor is 'C'. Let at at time of charging the capacitor charge on the capacitor is q' and at that time potential difference between its points is V',

Then

V' = q'/C

Let the work done in giving more very small volume of charge dq is dW,

So,

dW = V' × dq

Putting the value of V' = q'/C

dW = q'/C × dq

Now, If the work done in charging the capacitor from 0 to q is W

Then,

$\begin{gathered}W=\int\limits^q_0{dW}\\\;\\W=\int\limits^q_0{\frac{q'}{C}.dW}\\\;\\W=\frac{1}{C}\int\limits^q_0{q'\;dq}\\\;\\W=\frac{1}{C}[\frac{{q'}^{2}}{2}]\limits^q_0\\\;\\W=\frac{1}{C}[\frac{q^2}{2}-0]\\\;\\W=\frac{1}{2}\frac{q^2}{C}\end{gathered}$

This work has been stored in the capacitor as its electric potential energy, So we can denote it by 'U'. Putting W = U

$U=\frac{1}{2}\frac{q^2}{C}$

Also putting q = CV,

$U=\frac{1}{2}CV^2$

Answer 2

Answer:

The energy stored in a capacitor can be expressed in three ways: Ecap=QV2=CV22=Q22C E cap = QV 2 = CV 2 2 = Q 2 2 C , where Q is the charge, V is the voltage, and C is the capacitance of the capacitor. The energy is in joules when the charge is in coulombs, voltage is in volts, and capacitance is in farads.