AC Electrics -Introduction to AC — Page 168, Lesson 169

Let’s start with the basics of AC electricity. I want to walk you through the key parameters that define any alternating current supply. First, frequency. Frequency is the number of complete cycles that occur each second. It’s measured in hertz (Hz). One cycle per second equals one hertz. In aircraft, constant-frequency AC supply systems usually operate at 400 Hz. Frequency depends on how many times a North pole and a South pole pass the armature in a given time period — in other words, it’s determined by the generator’s construction and its speed. To calculate the frequency of a generator’s output, we use this formula: Frequency (in hertz) = (Number of Poles ÷ 2) × (RPM ÷ 60 seconds) Here, the number of poles is the total of all North and South poles that make up the generator’s field. RPM is the speed of rotation in revolutions per minute. Let’s take an example: an 8-pole generator rotating at 6000 RPM will have an output frequency of (8 ÷ 2) × (6000 ÷ 60) = 4 × 100 = 400 hertz. That matches the standard aircraft AC frequency. Next, period. The period is the time it takes for one complete cycle to occur. It’s simply the reciprocal of frequency: Period (T) = 1 ÷ f seconds So if frequency is 400 Hz, the period is 1/400 of a second. Now, amplitude or peak value. The amplitude of a sine wave is the maximum value it reaches during one cycle. That’s the highest point the voltage or current attains. Then we come to a very important concept: Root Mean Square value, or RMS value. The RMS value is the effective value of an alternating current, calculated by comparing it with direct current. The comparison is based on the amount of heat produced by each current under identical conditions. Here’s the key idea: a DC current of 1 amp will make a resistor hotter than an AC current with a peak value of 1 amp. So to make the resistor just as hot with AC, the AC’s peak value must be higher — so that its effective value equals 1 amp. That effective value is the RMS value. How do we find it? We take a number of instantaneous values of voltage or current during a half cycle. We square each of those values, find their mean (average), and then take the square root of that mean. That gives us the Root of the Mean of the Squares — the RMS value. Another way to think about it: the voltage (or current) rises from zero to maximum over 90° of phase angle. The average value occurs at the midway point, which is 45°. Since the values follow a sine curve, the value at 45° is the peak value multiplied by the sine of 45°, which is 0.707. So for a sine wave, the RMS value is related to the peak value by that factor of 0.707. That gives us the formula: RMS value = Peak value × 0.707 (for a sine wave). This relationship is fundamental to understanding how AC power is measured and compared to DC.