Resistor

For a resistor, we have the relation:

That is, the ratio of the instantaneous voltage and current associated with a resistor is the value of the DC resistance denoted by R. Since R is constant and real, it follows that if v(t) is sinusoidal, i(t) is also sinusoidal with the same frequency and phase. Thus, we have that the impedance of a resistor is equal to R:

Capacitor

For a capacitor, we have the relation

Now, Let

It follows that

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Missing part of the demonstration:

As an alternative to this demonstration, one could invoke the rule that a derivative of a real function becomes a multiplication by jw of its phasor transform.

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Using phasor notation and the result above, write our first equation as:

It follows that the impedance of a capacitor is

Inductor

For the inductor, we have:

By the same reasoning used in the capacitor example above, it follows that the impedance on an inductor is:

See also

• Electrical impedance