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.
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| RLC SERIES CIRCUIT |
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.
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| PHASOR DIAGRAM OF RLC SERIES CIRCUIT |
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.
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 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.
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
