# Impedance, Admittance, Conductance and Susceptance

If we take an arbitrary impedance, such as:

Z = a + bj

Then admittance is defined as the reciprocal of impedance, and is given by:

Y = 1 / Z

So, for an impedance a + bj we can write:

Y = 1 / a + bj

Multiplying above and below by a - bj we get

Y = (a - bj) / ((a - bj)(a + bj))

Y = (a - bj) / (a2 - (b2)(j2))

Y = (a - bj) / (a2 + b2)

Y = [a / (a2 + b2)] + [ - b / (a2 + b2)] j

We call the real part conductance, G, and the imaginary part susceptance, B. So,

G = a / (a2 + b2)

B = - b / (a2 + b2)

Note that susceptance has the opposite sign to its equivalent reactance.

Conductance and susceptance are measured in Siemens. This unit was previously known as the "mho" (the unit Ohm spealt backwards).

Term Equivalent Term
Impedance Admittance
Resistance Conductance
Reactance Susceptance

If we now compare the ideal resistor, capacitor and inductor we have:

Impedance Admittance
Real Imaginary Real Imaginary
Resistance Reactance Conductance Susceptance
Resistor a 0 1 / a 0
Capacitor 0 -bj 0 (1 / b) j
Inductor 0 +bj 0 - (1 / b) j
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