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In a series LCR circuit with , $$R = 20\,\Omega$$, $$L = 1.6$$ H, $$C = 40\,\mu$$F is connected to a variable frequency a.c. source. The inductive reactance at resonant frequency is ____________ $$\Omega$$.
Correct Answer: 200
$$\omega_r = \frac{1}{\sqrt{LC}}$$
$$\omega_r = \frac{1}{\sqrt{1.6 \times 40 \times 10^{-6}}}$$
$$\omega_r = \frac{1}{\sqrt{64 \times 10^{-6}}} = \frac{1}{8 \times 10^{-3}} = 125 \text{ rad/s}$$
$$X_L = \omega_r L$$
$$X_L = 125 \times 1.6 = 200 \ \Omega$$
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