Impedance - the overall resistance in an AC Circuit

Consider what happens when resistors, capacitors, and inductors are combined in series in one RLC circuit.

The overall resistance to the current in an RLC circuit is known as the impedance, Z. The impedance is found by adding as vectors the resistance, the capacitive reactance, and the inductive reactance. We need to add these as vectors because of the phase relationships. Resistors like the voltage and current to be in phase. Capacitors like the current to lead the voltage by 90o, and inductors like the current to lag the voltage by 90o. When all three components are combined into one circuit, there has to be some compromise.

To figure out the impedance, and to determine the phase between the voltage and current, draw an impedance triangle. The resistance R is drawn along the +x-axis of an x-y coordinate system. The inductive reactance is at 90o to this, on the +y-axis. The capacitive reactance is drawn along the -y-axis. The impedance, Z, is the sum of these vectors, and is given by:

Z = [(XL - XC)2 + R2]1/2

The current and voltage in an RLC circuit are related by V = IZ. The phase relationship between the current and voltage can be found from the impedance triangle: it's the angle between the impedance, Z, and the resistance, R:

tan(f) = (XL - XC)/R

If the phase angle is positive, the voltage leads the current by that angle. If the angle is negative, the voltage lags the currents.