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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 = Ö 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 = 0º). And for the capacitor the voltage is always lagging the current by 90º ( qC = 90º).  It is the phase of the total circuit impedance ( q ) that varies between 0º and 90º.

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 = Ö 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