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

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Angular frequency, ω = 2 π f = 100 π r a d s − 1 Here, inductive reactance X L ​ = ω L = ( 100 π ) ( 100 × 1 0 − 3 ) = 10 π Ω And capacitive reactance X C ​ = ω C 1 ​ = ( 100 π ) × ( 100 × 1 0 − 6 ) 1 ​ = π 100 ​ Ω = 10 π Ω Now, impedance of the series circuit is Z = R 2 + ( X L ​ − X C ​ ) 2 ​ = R = 10Ω Therefore, I RMS ​ = Z V RMS ​ ​ , = 10 220 ​ = 22 A

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