LCR Series Circuit
ElectroMagnetism > AC Circuits
LCR circuit LCR circuit An LCR circuit that have inductors (bottom right), capacitors(brown) and resistors.

LCR Series Circuit: An LCR series circuit is the one which has an Inductor, Capacitor and Resistance which are connected in series. Same amount of current flows through these three components and the voltage drops across each component will be equal to the supply voltage of the AC source.

If we consider an inductor in AC circuit, the voltage across the inductor “leads” the current by 90°. Like wise, In AC circuit with a capacitor, the voltage across the capacitor “lags” the current by 90°.

Now, in LCR circuit, both of these are combined in series which have individual voltage drops across each circuit element R, L and C element and will be “out–of–phase” with each other given by the following cases:

  1. The instantaneous voltage across the resistor will be in phase with the current.
  2. The instantaneous voltage across an inductor, leads the current by 90°.
  3. The instantaneous voltage across a capacitor lags the current by 90°.
  4. Hence, both the voltages across the inductor and the capacitor will be out of phase by 180° opposing each other.
LCR in Series LCR in Series

The amplitude of the source voltage across the three components will be different and are made of three individual component voltages. We cannot add the voltages across the components to get the source voltage, due to the reason that they are not in same phase with respect to each other. Thus the source voltage is the vector phasor sum of the three component voltages.

In this LCR circuit we have Inductive reactance, capacitive reactance to determine the over all impedance of the circuit. Let us look at the three possible cases:

  1. If the capacitive reactance is greater than the inductive reactance, then the overall circuit reactance is capacitive which gives rise to a leading phase angle.
  2. If the inductive reactance is greater than the capacitive reactance, then the overall circuit reactance is inductive which gives rise to the series circuit with a lagging phase angle.
  3. If the reactances of the two components are same, then the angular frequency at which this occurs is known as the resonant frequency and hence resonance is produced.

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