Question

what is the electrical energy of a capacitor C charged to potential V.?​

Answer 1

Answer:

The value of electrical energy of a Capacitor C charged to potential V is given by $\frac{1}{2} CV^{2}$

Explanation:

Let dW represent the amount of labor required to charge the capacitor by a very small amount, dq.

Thus, dW can be written as,

dW = V dq

Where V is the potential difference and dq is the small charge.

Also, we know that q = CV

$dW = \frac{q}{C} dq$

Now, we integrate the expression to calculate the total work done,

$\int\limits^W_0 {dW} \, = \frac{1}{C} \int\limits^q_0 {q} \, dq$

After integration, we get:

$W = \frac{q^{2} }{2C}$

Now, again we know that q = CV, then

$W = \frac{(CV)^{2} }{2C}$

Simplifying the expression, we get,

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

Therefore, the value of electrical energy of a Capacitor C charged to potential V is given by $\frac{1}{2} CV^{2}$

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