Friday 7-26-96
We talked a lot about how resistors work in DC circuits, opposing the current. Resistors work much the same way in AC circuits. Consider, then, the voltage and current in an AC circuit with just a resistor and an AC power source.
Instead of a constant voltage supplied by a battery, the voltage in an AC circuit oscillates in a sine wave pattern, varying with time as:
V = Vo sin wt
In a household circuit, the frequency is 60 Hz. The angular frequency, w, is related to the frequency by a factor of 2 pi:
w = 2 pi f
So, w = 120 pi for a household circuit.
Vo represents the maximum voltage, which is about 170 volts in a household circuit. We talk of a household voltage of 110 - 120 volts; this number is a kind of average value of the voltage. The particular averaging method used is something called root mean square (square the voltage to make everything positive, find the average, take the square root), or rms. Voltages and currents for AC circuits are expressed as rms values. For a sine wave, the relationship between the peak and the rms average is:
rms value = 0.707 peak value
The relationship V = IR holds for resistors in an AC circuit, so
I = V/R = (Vo/R) sin wt = Io sinwt
In AC circuits we'll talk a lot about the phase of the current relative to the voltage. In a circuit which only involves resistors, the current and voltage are in phase with each other, because peak voltage is reached at the same instant as peak current. In circuits which have capacitors and inductors (coils) the phase relationships will be quite different.