In a series LCR circuit, the inductance, capacitance and resistance are $$L = 100$$ mH, $$C = 100$$ $$\mu$$F and $$R = 10$$ $$\Omega$$ respectively. They are connected to an AC source of voltage $$220$$ V and frequency of $$50$$ Hz. The approximate value of current in the circuit will be ______ A.

$$\omega = 2\pi f = 2 \times 3.14 \times 50 = 314\ \text{rad/s}$$

$$X_L = \omega L = 314 \times 100 \times 10^{-3} = 31.4\ \Omega$$

$$X_C = \frac{1}{\omega C} = \frac{1}{314 \times 100 \times 10^{-6}} = \frac{10^4}{314} \approx 31.85\ \Omega$$

$$Z = \sqrt{R^2 + (X_L - X_C)^2}$$

$$\implies Z = \sqrt{10^2 + (31.4 - 31.85)^2} = \sqrt{100 + (-0.45)^2} = \sqrt{100 + 0.2025} \approx 10\ \Omega$$

$$I_{\text{rms}} = \frac{V_{\text{rms}}}{Z} = \frac{220}{10} = 22\ \text{A}$$