**What is 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.

#### A RLC series circuit having resistance R , inductance L and capacitance C is shown in the figure below.

RLC SERIES CIRCUIT |

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Let, **V** = RMS value of applied voltage.

** I **= RMS value of current

**Vr** = Voltage drop across resistance = I*R

**Vₗ **= Voltage across inductance = I*X

**Vc** = Voltage drop across capacitance = I*Xc

Phasor diagram of series RLC circuit is shown in figure.

* Voltage drop across R is in phase with the current.

* Voltage drop across L leads the current by 90 degree.

* Voltage drop across C lags behind current by 90 degree.

PHASOR DIAGRAM OF RLC SERIES CIRCUIT |

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As seen from the phasor diagram that Vₗ and Vc are 180 degree out of phase, they are direct opposite to each other. So effective voltage will be *(Vₗ-Vc)*.

Applied voltage is phasor sum of the voltage across resistance & effective voltage.

*(Vₗ-Vc)*

**V = √{(Vr)² + (Vₗ -Vc)²}**

**V = √{(I*R)² + (I*Xₗ – I*Xc)²}**

**V = I * √{(R)² + (Xₗ – Xc)²}**

**I = V / √{(R)² + (Xₗ- Xc)²}**

The quantity √{(R)² + (Xₗ – Xc)²} represents **impedance,Z of the RLC series circuit.**

**Z = √{(R)² + (Xₗ – Xc)²}.**

__Power factor of RLC Series Circuit__

__Power factor of RLC Series Circuit__

*Power factor is defined as the cosine of the angle between voltage and current.* As seen from the phasor diagram, applied voltage is lagging behind the current by angle ⲫ.

*Power factor is defined as the cosine of the angle between voltage and current.*

So from phasor diagram,

**Power Factor = cosⲫ = Vr / V.**

**cosⲫ = I*R / I*√{(R)² + (Xₗ – Xc)²}.**

**cosⲫ = R / √{(R)² + (Xₗ – Xc)²}.**

**cosⲫ = R/Z = Resistance / Impedance.**

Hence,

**– Power factor = Resistance / Impedance**

– Power factor = True Power / Apparent Power

*If Xc > Xₗ , then current leads the voltage.*

*If Xc > Xₗ , then current leads the voltage.*

**If ****Xc < Xₗ , then current lags behind the voltage.**

**If**

**Xc < Xₗ , then current lags behind the voltage.**

**If ****Xc = Xₗ , then current is in phase with voltage and power factor is unity.**

**If**

**Xc = Xₗ , then current is in phase with voltage and power factor is unity.**