What is RC Series Circuit? Phasor Diagram and Power Curve

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RC Series Circuit
RC Series Circuit

What is RC Series Circuit?

A circuit that contains pure resistance R ohms connected in series with a pure capacitor of capacitance C farads is known as RC Series Circuit. A sinusoidal voltage is applied and current I flows through the resistance (R) and the capacitance (C) of the circuit.

A RL series circuit having resistance R and capacitance C is shown in the figure below.

RC series circuit
RC SERIES CIRCUIT

Let, V = RMS value of applied voltage.
 I = RMS value of current
Vr = Voltage drop across resistance = I*R
Vc = Voltage drop across capacitance =  I*Xc

We know that current in the pure capacitance current leads the voltage by 90 degree. Therefore,current I is 90 degree ahead of Voltage drop across capacitance, Vc.

Phasor diagram of series RC circuit is shown in figure.

* Voltage drop across R is in phase with the current
* Voltage drop across C lags behind current by 90.

Phasor diagram of rc series circuit
PHASOR DIAGRAM OF RC SERIES CIRCUIT


*Note that current leads the applied voltage in RC Series Circuit.

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

V = √{(Vr)² + (Vc)²}

V = √{(I*R)² + (I*Xc)²}

V = I * √{(R)² + (Xc)²}

I = V / √{(R)² + (Xc)²}

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

Z = √{(R)² + (Xc)²}.

Power factor of RC 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.

So from phasor diagram,

Power Factor = cosⲫ = Vr / V.

cosⲫ = I*R / I*√{(R)² + (Xc)²}.

cosⲫ = R / √{(R)² + (Xc)²}.

cosⲫ = R/Z = Resistance / Impedance.

Hence,
– Power factor = Resistance /  Impedance

– Power factor = True Power / Apparent Power

READ HERE  DC Shunt Motors: Characteristics & Performance

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