RLC Series Circuit

When a pure resistance of R ohms, a pure inductance of L Henry and a pure capacitance of C farads are connected together in series combination with each other then RLC Series Circuit is formed. As all the three elements are connected in series so, the current flowing through each element of the circuit will be the same as the total current I flowing in the circuit.

Contents:

• RLC Circuit
• Phasor Diagram of RLC Series Circuit
• Steps to draw the Phasor Diagram of the RLC Series Circuit
• Phase Angle
• Power in RLC Series Circuit
• Impedance Triangle of RLC Series Circuit

The RLC Circuit is shown below:

In the RLC Series circuit

X_L = 2πfL and X_C = 1/2πfC

When the AC voltage is applied through the RLC Series circuit the resulting current I flows through the circuit, and thus the voltage across each element will be:

• V_R = IR that is the voltage across the resistance R and is in phase with the current I.
• V_L = IX_L that is the voltage across the inductance L and it leads the current I by an angle of 90 degrees.
• V_C = IX_C that is the voltage across capacitor C and it lags the current I by an angle of 90 degrees.

Phasor Diagram of RLC Series Circuit

The phasor diagram of the RLC series circuit when the circuit is acting as an inductive circuit that means (V_L>V_C) is shown below and if (V_L< V_C) the circuit will behave as a capacitive circuit.

Steps to draw the Phasor Diagram of the RLC Series Circuit

• Take current I as the reference as shown in the figure above
• The voltage across the inductor L that is V_L is drawn leads the current I by a 90-degree angle.
• The voltage across the capacitor c that is V_c is drawn lagging the current I by a 90-degree angle because in capacitive load the current leads the voltage by an angle of 90 degrees.
• The two vector V_L and V_C are opposite to each other.

Where, It is the total opposition offered to the flow of current by an RLC Circuit and is known as Impedance of the circuit.

Phase Angle

From the phasor diagram, the value of phase angle will be

Power in RLC Series Circuit

The product of voltage and current is defined as power.Where cosϕ is the power factor of the circuit and is expressed as:

The three cases of RLC Series Circuit

• When X_L > X_C, the phase angle ϕ is positive. The circuit behaves as RL series circuit in which the current lags behind the applied voltage and the power factor is lagging.
• When X_L < X_C, the phase angle ϕ is negative, and the circuit acts as a series RC circuit in which the current leads the voltage by 90 degrees.
• When X_L = X_C, the phase angle ϕ is zero, as a result, the circuit behaves like a purely resistive circuit. In this type of circuit, the current and voltage are in phase with each other. The value of the power factor is unity.

Impedance Triangle of RLC Series Circuit

When the quantities of the phasor diagram are divided by the common factor I then the right angle triangle is obtained known as impedance triangle. The impedance triangle of the RL series circuit, when (X_L > X_C) is shown below:

If the inductive reactance is greater than the capacitive reactance than the circuit reactance is inductive giving a lagging phase angle.

Impedance triangle is shown below when the circuit acts as an RC series circuit (X_L< X_C)

When the capacitive reactance is greater than the inductive reactance the overall circuit reactance acts as capacitive and the phase angle will be leading.

Applications of RLC Series Circuit

The following are the application of the RLC circuit:

• It acts as a variable tuned circuit
• It acts as a low pass, high pass, bandpass, bandstop filters depending upon the type of frequency.
• The circuit also works as an oscillator
• Voltage multiplier and pulse discharge circuit

This is all about the RLC circuit.