Electrical Resistance and Conductance - AC Circuits - Impedance and Admittance

Impedance and Admittance

When an alternating current flows through a circuit, the relation between current and voltage across a circuit element is characterized not only by the ratio of their magnitudes, but also the difference in their phases. For example, in an ideal resistor, the moment when the voltage reaches its maximum, the current also reaches its maximum (current and voltage are oscillating in phase). But for a capacitor or inductor, the maximum current flow occurs as the voltage passes through zero and vice-versa (current and voltage are oscillating 90° out of phase, see image at right). Complex numbers are used to keep track of both the phase and magnitude of current and voltage:

where:

• t is time,
• V(t) and I(t) are, respectively, voltage and current as a function of time,
• V₀, I₀, Z, and Y are complex numbers,
• Z is called impedance,
• Y is called admittance,
• Re indicates real part,
• is the angular frequency of the AC current,
• is the imaginary unit.

The impedance and admittance may be expressed as complex numbers which can be broken into real and imaginary parts:

where R and G are resistance and conductance respectively, X is reactance, and B is susceptance. For ideal resistors, Z and Y reduce to R and G respectively, but for AC networks containing capacitors and inductors, X and B are nonzero.

for AC circuits, just as for DC circuits.