# 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:

**X _{L }= 2πfL** and

**X**

_{C}= 1/2πfCWhen 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.

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.

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