Free-Ed: Basic Electronics Fundamentals

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 + X_C²

Where:

Z = RL circuit impedance

R = Resistor value

X_C = Capacitive reactance

If you know the values for R and X_C, you can solve the equation directly. In most practical situations, however, you know the values of C and f, and must calculate X_C 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 (q_R = 0�). And for the capacitor the voltage is always lagging the current by 90� ( q_C = �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 X_C

R

Where:

q = Phase angle in degrees or radians

X_C = 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:

V_T = � V_R² + V_CL²

Where:

V_T = Source voltage

V_R = Resistor voltage

V_C = Capacitor voltage

Equation

The voltage phase angle for a series RL circuit is:

q = tan^-1 V_C

V_R

Where:

q = Phase angle in degrees or radians

V_C = Capacitor voltage

V_R = 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:

I_T = I_R = I_C = V_T

Z

Where:

I_T = total current

I_R = Resistor current

I_C = Capacitor Current

V_T = Total Voltage

Z = Circuit impedance

Analyzing Series RC Circuits