Resistor AC Response
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
This is 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: