The
basic circuit on the left side, where the source voltage Vs is a AC Resistive Circuits
I. Voltage and Current
The
basic circuit on the left side, where the source voltage Vs is a
sinusoidal waveform will be used to represent a general resistive
AC circuit.
All the laws and formulas that apply to DC circuits also apply to AC circuits. Furthermore they apply exactly
the same way to AC Resistive circuits. This is true, because resistors are linear components and their characteristics do not depend on frequency. Hence, the current in the above circuit is simply I = V/R.
The waveform representing the current is smaller than that one representing the voltage because of the 1/R factor given by Ohm's law. For purely resistive circuits the current and voltage are in phase with one another.
This is shown in Fig.1 below, where the Yellow waveform represents the voltage and the Green waveform represents the current in the circuit. Note that they are in phase with one another!
Fig.1
II. AC Resistor circuits
On the left is a series-parallel AC circuit
containing several resistors. The same rules that
apply to DC circuits apply to AC resistive circuits.
To deal with a circuit such as the one given above the resistors can be combined to obtain an equivalent
resistance Req . Also voltage dividers and current dividers can be used just as in DC circuits. Kirchhoff's Current Law and Voltage Law apply just in exactly the same way as in DC circuits. Ohm's law and the power formula can also be applied just as before. Hence, there is nothing unfamiliar about resistor AC circuits, except that all the voltages and currents are sinusoidal waveforms with specific Peak or RMS amplitudes and a frequency the same as the frequency of the source voltage Vs.
III. Power in AC Resistive circuits
The Power formula indicates that P = I·V, the only distinction with DC circuits is that here it must be noted whereas this is a Peak value of power (if the current and voltage are Peak values) or if it is an RMS value for power (in the case that both current and voltage are RMS values).
How then are the RMS and Peak values of power related? Well, since Irms = Ip/√2 and Vrms = Vp/√2; and also since Prms = Irms · Vrms , then Prms = Ip/√2 · Vp/√2 = (Ip·Vp)/2 = Pp/2.
Hence, the answer is that the RMS value of the power in an AC resistive circuit is one half its peak value. This is the only distinction worth noting between power in AC resistive circuits and in DC circuits.