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 to  and current I flows through the resistance (R) and the capacitance (C) of the circuit.The RC Series circuit is shown in the figure below

R-C-SERIES-circuitWhere,

  • VR – voltage across the resistance R
  • VC – voltage across the capacitor C
  • V – total voltage across the RC Series circuit

Contents:

Phasor Diagram of RC Series Circuit

The phasor diagram of the RC Series circuit is shown below

PHASOR-DIAGRAM-OF-R-C-SERIES-CKT-compressor

Steps to draw a Phasor Diagram

The following steps are used to draw the phasor diagram of RC Series circuit

  • Take the current I (r.m.s value) as a reference vector
  • Voltage drop in resistance VR = IR is taken in phase with the current vector
  • Voltage drop in capacitive reactance VC = IXC is drawn 90 degrees behind the current vector, as current leads voltage by 90 degrees in pure capacitive circuit)
  • The vector sum of the two voltage drops is equal to the applied voltage V (r.m.s value).

Now, VR = IR and VC = IXC

Where, XC = I/2πfC

In right triangle OAB
RC-SERIES-CKT-EQ1

Where,
RC-SERIES-CKT-EQ2

Z is the total opposition offered to the flow of alternating current by an RC Series circuit and is called impedance of the circuit. It is measured in ohms (Ω).

Phase angle

From the phasor diagram shown above it is clear that the current in the circuit leads the applied voltage by an angle ϕ and this angle is called the phase angle.

RC-SERIES-CKT-EQ3

Power in RC Series Circuit

If the alternating voltage applied across the circuit is given by the equation
RC-SERIES-CKT-EQ4

Then,
RC-SERIES-CKT-EQ5

Therefore, the instantaneous power is given by p = vi

Putting the value of v and i from the equation (1) and (2) in p = vi

RC-SERIES-CKT-EQ6

The Average power consumed in the circuit over a complete cycle is given by

RC-SERIES-CKT-EQ7

Where, cosϕ is called the power factor of the circuit.

RC-SERIES-CKT-EQ8

Putting the value of V and cosϕ from the equation (3) the value of power will be

RC-SERIES-CKT-EQ9

From the equation (4) it is clear that the power is actually consumed by the resistance only and the capacitor does not consumes any power in the circuit.

Waveform and Power Curve of the RC Series Circuit

The waveform and power curve of the RC Circuit is shown below
RC-SERIES-CIRCUIT-WAVEFORMThe various points on the power curve is obtained from the product of the instantaneous value of voltage and current. The power is negative between the angle (180◦ – ϕ) and 180◦ and between (360◦ -ϕ) and 360◦ and in the rest of the cycle the power is positive. Since the area under the positive loops is greater than that under the negative loops, therefore the net power over a complete cycle is positive.

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