A capacitor (C) and a resistor (R) are connected in series with an a.c, source of voltage of frequency 50 Hz. The potential difference across C and R are respectively 120 V and 90 V. The current in the circuit is 3A. Calculate () impedance of the circuit, (i) value of the inductance which when connected in series with Cand R will make the power fador of the circuit unity.

Explanation

To solve the problem step by step, we will first calculate the impedance of the circuit and then find the value of the inductance required to make the power factor unity.

### Step 1: Calculate the total voltage (V) across the circuit

The total voltage across the circuit can be calculated using the Pythagorean theorem, since the voltages across the resistor (V_R) and capacitor (V_C) are perpendicular to each other in an AC circuit.

\[
V = \sqrt{V_R^2 + V_C^2}
...