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A resistance $R = 12 Ω$ , inductance L = 2H and capacitance C = 5 mF are connected in series to an AC generator of frequency 50 Hz.

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the inductive reactance is less than capacitive reactance

the resonance frequency of the circuit is $\frac{1}{0.2 π}$ Hz

at resonance, the circuit impedance is zero

at resonance, the circuit impedance is 12 ohm

answer is B, C.

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Detailed Solution

Circuit impedance at resonance, $Z = R = 12 Ω$ .

Resonance frequency,

$\begin{array}{l} f_{0} = \frac{1}{2 π \sqrt{LC}} = \frac{1}{2 π \sqrt{2 \times (5 \times 10^{- 3})}} = \frac{1}{0 .2 π} \end{array} Hz$ .

$\begin{array}{l} Inductive reactance X_{L} = 2 πfL = 2 π \times 50 \times 2 = 200 π Ω \\ Capacitive reactance X_{C} = \frac{1}{2 πfC} = \frac{1}{2 π \times 50 \times (5 \times 10^{- 3})} = \frac{2}{π} Ω \\ ∴ X_{L} > X_{C} \end{array}$

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