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AC Components and Circuits
AC RC Circuits

Section 7-2 Series RC Circuit Analysis


 

 

 

Impedance in Series RC Circuits


An ideal series RC circuit.


Phasor diagram for series RL circuits.

 

 

Equation

The impedance of a series RC circuit is:

Z = R2 + XC2

Where:

Z = RL circuit impedance
R = Resistor value
XC = Capacitive reactance

If you know the values for R and XC, you can solve the equation directly. In most practical situations, however, you know the values of C  and f, and must calculate XC in order to use the series-Z equation.

Since this is a series circuit, the magnitude of the current is the same at all point. It's the voltage that is subject to phase shifting. Recall there is no phase shift for a resistor (qR = 0). And for the capacitor the voltage is always lagging the current by 90 ( qC = 90).  It is the phase of the total circuit impedance ( q ) that varies between 0 and 90.

Equation

The impedance phase angle for a series RC circuit is:

q = tan-1 XC
R

Where:

q = Phase angle in degrees or radians
XC = Capacitive reactance
R = Resistor value

Examples

Endless Examples & Exercises

Work these problems until you are confident you have mastered the procedures.
  • All angles are expressed in degrees.
  • Round answers to the nearest tenth.

 

 

 

 

 

Voltages in Series RC Circuits

 

 

 

Equation

The total voltage of a series RC circuit is:

VT = VR2 + VCL2

Where:

VT = Source voltage
VR = Resistor voltage
VC = Capacitor voltage

 

 

Equation

The voltage phase angle for a series RL circuit is:

q = tan-1 VC
VR

Where:

q = Phase angle in degrees or radians
VC = Capacitor voltage
VR = Resistor voltage

 

Current in Series RC Circuits

 

The currents in a series RC are equal, and there are several ways to that value.

Equation

Current in a series RC circuit:

IT = IR = IC = VT
Z

Where:

IT = total current
IR = Resistor current
IC = Capacitor Current
VT = Total Voltage
Z = Circuit impedance

 

 

 

Analyzing Series RC Circuits

 

 

 

 

David L. Heiserman, Editor

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All Rights Reserved

Revised: June 06, 2015