The figure shows a series LCR circuit: For such a circuit, the impedance \( Z \) is given by, \(...
0The figure shows a series LCR circuit:
For such a circuit, the impedance \( Z \) is given by, \( Z=\sqrt{R^{2}+\left(X_{L}-X_{C}\right)^{2}} \) where \( X_{L} \) and \( X_{C} \) are inductive and capacitive resistances respectively.
As the frequency of a.c. is increased, at a particular frequency \( X_{L} \) become, equal to \( X_{C} \). For that frequency maximum current occurs. This is because impedance becomes equal to its least value \( R \). Current through the circuit is given by \( I=V / R \). The circuit behaves like a pure resistive circuit and current and voltage will be in phase. This is called resonance. Frequency of a.c. at which resonance occurs is called resonant frequency. If frequency is less than the resonant frequency, then the capacitive reactance will be more. The circuit will be capacitive in nature and current leads voltage. On the other hand, if frequency is more than the resonant frequency, inductive reactance will be more. Circuit is inductive in nature and current lags the voltage.
An LCR circuit with a resistance \( 50 \Omega \) has a resonant angular frequency \( 2 \times 10^{3} \mathrm{rad} / \mathrm{s} \). At resonance, the voltage across the resistance and inductance are \( 25 \mathrm{~V} \) and \( 20 \mathrm{~V} \) respectively. Then At angular frequency \( 10^{3} \mathrm{rad} / \mathrm{s} \), the nature of circuit:
(A) Inductive
(B) Capacitive
(C) Resistive
(D) None of these
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