## AC Voltage Applied to a Series LCR Circuit – Class 12 | Chapter – 7 | Physics Short Notes Series PDF for NEET & JEE

AC Voltage Applied to a Series LCR Circuit: A series LCR circuit is a circuit that consists of a resistor (R), an inductor (L), and a capacitor (C) connected in series with an AC voltage source. When an AC voltage is applied to a series LCR circuit, the behavior of the circuit depends on the frequency of the AC voltage and the values of R, L, and C.

## AC Voltage Applied to a Series LCR Circuit

At low frequencies, the reactance of the capacitor is high, and the reactance of the inductor is low, so the capacitor dominates the behavior of the circuit. The current lags the voltage by almost 90 degrees, and the circuit behaves like a capacitive circuit. At this frequency, the capacitor charges and discharges rapidly, and the current is largely determined by the capacitive reactance, Xc.

As the frequency increases, the reactance of the capacitor decreases, and the reactance of the inductor increases. At a certain frequency, called the resonance frequency, the reactance of the capacitor equals the reactance of the inductor, and the current is at its maximum. At this frequency, the circuit behaves like a purely resistive circuit, and the current is in phase with the voltage.

As the frequency continues to increase, the reactance of the inductor dominates, and the current leads the voltage by almost 90 degrees. The circuit behaves like an inductive circuit, and the current is largely determined by the inductive reactance, Xl.

The behavior of a series LCR circuit is important in many applications, such as in tuning circuits and filter circuits. By using phasor analysis, the voltage and current waveforms in a series LCR circuit can be analyzed and calculated, making it possible to predict the behavior of the circuit and design components for optimal performance. The resonance frequency of the circuit can be calculated using the formula:

fres = 1 / (2π√(LC))

where fres is the resonance frequency, L is the inductance of the inductor, C is the capacitance of the capacitor, and π is approximately 3.14159.

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