Resistor AC Response

Impedance Calculate

Examine Capacitor Inductor

Contribution to complex impedance Phasor diagram

For ordinary currents and frequencies the behavior of a resistor is that of a dissipative element which converts electrical energy into heat. It is independent of the direction of current flow and independent of the frequency. So we say that the AC impedance of a resistor is the same as its DC resistance. That assumes, however, that you are using the rms or effective values for the current and voltage in the AC case.

RMS and Effective Values

Circuit currents and voltages in AC circuits are generally stated as root-mean-square or rms values rather than by quoting the maximum values. The root-mean-square for a current is defined by

That is, you take the square of the current and average it, then take the square root. When this process is carried out for a sinusoidal current

Since the AC voltage is also sinusoidal, the form of the rms voltage is the same. These rms values are just the effective value needed in the expression for average power to put the AC power in the same form as the expression for DC power in a resistor. In a resistor where the power factor is equal to 1:

Since the voltage and current are both sinusoidal, the power expression can be expressed in terms of the squares of sine or cosine functions, and the average of a sine or cosine squared over a whole period is = 1/2.