(a) Prove that the current flowing through an ideal inductor connected across a.c. source, lags the voltage in phase by `pi/2`.
(b) An inductor of self inductance 100 mH, and a bulb are connected in series with a.c. sources of rms voltage 10 V, 50 z. It is found that effective voltage of the circuit leads the current in phase by `pi/4`.
Calculate the inductance of the inductor used and average power dissipated in the circuit, if a current of 1 A flows in the circuit.

Explanation

### Step-by-Step Solution

#### Part (a): Proving that the current lags the voltage by π/2 in an ideal inductor

1. **Define the current through the inductor**:
Let the current flowing through the inductor be represented as:
\[
I(t) = I_0 \sin(\omega t)
...