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Impedance and Admittance

 

 

 
 

         

Impedance (Z) is the over-all measure of the ability of a circuit to resist the flow of alternating current under a given a.c. voltage excitation. It may be expressed as Z = V / I where V and I are the a.c. voltage applied to and current flowing through the circuit. Its unit of measurement is the ohm (volt/ampere).

       

 

Impedance consists of two components - resistance and reactance.  A good understanding of what impedance is and how it is related to resistance and reactance is important in the analysis of voltage-current relationships in an AC circuit that consists of resistors as well as reactive components (capacitors and inductors). For more details about resistance and reactance, please see these separate articles:  Resistance; Reactance.

  

In an AC circuit that consist of a resistance R in series with a reactance X, the following equations apply:

|Z| = SQRT(R2 + X2);

θ = tan-1(X / R)

p.f. = cos θ = R / Z

where:

Z is the impedance of the circuit;

R is the resistance of the circuit;

X is the reactance of the circuit;

θ is the phase angle between the voltage and current signals;

and p.f. is the power factors of the circuit, which is the ratio of true power to apparent power of the circuit.

  

In an AC circuit that consist of a resistance R in parallel with a reactance X, the following equations apply:

|Z| = RX / SQRT(R2 + X2);

θ = tan-1(R / X)

p.f. = cos θ = Z/R

where:

Z is the impedance of the circuit;

R is the resistance of the circuit;

X is the reactance of the circuit;

θ is the phase angle between the voltage and current signals;

and p.f. is the power factors of the circuit, which is the ratio of true power to apparent power of the circuit.

  

As shown in the equations above, the presence of either a capacitor or an inductor (or both) in a circuit produces a phase shift θ between the voltage and current ac signals. This phase shift between voltage and current results in reactive power which can not do real work. In such a case, the true power of the circuit is just a fraction (denoted by the power factor) of its apparent power.

    

Admittance (Y) is the reciprocal of reactance, i.e., Y = 1 / Z.  The unit of measurement for admittance is the siemens (S).

       

 

   

See Also:   Resistance;  Reactance;  Ohm's Law