# RLC Series Circuit

The **RLC Series Circuit** is defined as 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. As all the three elements are connected in series so, the current flowing in each element of the circuit will be 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

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 the 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.

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 a 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 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 a RC series circuit (X_{L}< X_{C})

When the capacitive reactance is greater than the inductive reactance the overall circuit reactance acts as a 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, band pass, band stop filters depending upon the type of frequency.
- The Circuit also works as an oscillator
- Voltage multiplier and pulse discharge circuit