A capacitor of unknown capacitance, a resistance of 100 ohm and an inductor of inductance `L = 4//pi^(2)` henry are connected in series across an a.c. source of 200 V, 50 Hz. Calculate the value of capactance and the current that flows in the circuit, when the current is in phase with the voltage.

Explanation

To solve the problem step-by-step, we will calculate the unknown capacitance \( C \) and the current \( I_{RMS} \) flowing in the circuit when the current is in phase with the voltage.

### Step 1: Identify Given Values
- Resistance \( R = 100 \, \Omega \)
- Inductance \( L = \frac{4}{\pi^2} \, \text{H} \)
- Voltage \( V_{RMS} = 200 \, \text{V} \)
- Frequency \( f = 50 \, \text{Hz} \)

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