RMS = PEAK VALUE — Page 168, Lesson 171

I want to walk you through the relationship between RMS and peak value in AC circuits, and then we'll look at how current and voltage behave together in an AC system. Let's start with the RMS value. RMS stands for Root Mean Square, and it's a way of expressing an AC voltage or current as an equivalent DC value that would produce the same heating effect in a resistor. The key formula you need is this: the RMS value equals the peak value divided by the square root of 2. Or, written another way, RMS equals 0.707 multiplied by the peak value. So if you know the peak voltage of a sine wave, you multiply it by 0.707 to get the RMS voltage. Now, why does this matter? Because most AC supply values you encounter are given in RMS terms. When you look at a domestic mains supply labelled 230 volts, that's the RMS value. And in general terms, ammeters and voltmeters are calibrated in RMS values as well. So when you read a measurement on an AC ammeter or voltmeter, the number you see is already the RMS value, not the peak. Now let's move to the relationship of current and voltage in an AC circuit. In any AC circuit, the current and voltage have the same frequency, and their waveform shape is similar. For example, if the voltage waveform is sinusoidal, then the current waveform is also sinusoidal. They both go up and down at the same rate. In a DC circuit, the current flow is directly affected by the applied voltage and the circuit resistance, following Ohm's Law: V equals I times R. That means current is directly proportional to voltage and inversely proportional to resistance. Simple enough. But AC circuits are different. There are very few AC circuits where the current is affected solely by the applied voltage and resistance. In those rare circuits, both the current and the voltage pass through zero and reach their peaks in the same direction at the same time. When that happens, we say the voltage and current are in phase, and the circuit is described as resistive. In most AC circuits, however, because the voltage and current are constantly changing, the current flow is influenced by two additional effects: the magnetic effect of inductance and the electrostatic effect of capacitance. These cause the current and voltage to become out of phase. That means although they still have the same frequency, the voltage and current do not pass through zero at the same time. The difference between corresponding points on the two waveforms is known as the phase difference or phase angle. We'll study inductive and capacitive circuits in detail later, but for now, understand that this phase shift is a fundamental behaviour of most AC circuits.