An inductor 200 mH, capacitor `500 mu F`, resistor 10 ohm are connected in series with a 100 V, variable frequency a.c. source. Calculate (i) frequency at which power factor of the circuit is unity (ii) current amplitude at this frequency (iii) Q factor.

Explanation

To solve the problem step by step, we will calculate the frequency at which the power factor of the circuit is unity, the current amplitude at this frequency, and the Q factor.

### Given Data:
- Inductance, \( L = 200 \, \text{mH} = 200 \times 10^{-3} \, \text{H} \)
- Capacitance, \( C = 500 \, \mu\text{F} = 500 \times 10^{-6} \, \text{F} \)
- Resistance, \( R = 10 \, \Omega \)
- Voltage, \( V = 100 \, \text{V} \)

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