Derive an experssion for the average power in LCR circuit connected to a.c. supply. Hence define power factor. Show that average power cousumed per cycle in an a.c. circuit conataining an ideal capacitor is zero.

Explanation

To derive an expression for the average power in an LCR circuit connected to an AC supply, we start with the sinusoidal voltage and current expressions.

### Step-by-Step Solution:

1. **Voltage and Current Representation**:
The voltage \( V(t) \) and current \( I(t) \) in an AC circuit can be represented as:
\[
V(t) = V_0 \sin(\omega t + \phi)
...