Electrical current is a directional movement of electrons, or any other charged particles in general, like positive and negative ions, and so on. Alternating current is an electrical current with variable direction. In practice, we use electrical current which amplitude varies periodically by sinusoidal law. The frequency of the alternating current is a measure for the velocity of changing the direction of the current. The frequency of the voltage network in Europe is 50 Hz, and in USA is 60 Hz.
Picture 1: A sinusoidal waveform of AC current/voltage
The waveform of the alternating current which amplitude varies periodically by sinusoidal law is represented on Picture 1. The mathematical equations for a sinusoidal alternating current are representing on Picture 2. The first equation shows the time dependence of AC current. Because sin function can vary from -1 to +1, that means that AC current varies from -Imax to +Imax, where Imax is the amplitude of the current signal, the maximum value. Second equation comes when we assume that the starting phase is 0. During one period of time T (the period is a reciprocal value of the frequency of the AC current, T = 1/f) AC current reaches one -Imax value and one +Imax value and two times is equal to zero. The angular frequency of the sinusoidal waveform is also shown on the Picture 2. If the frequency is f = 50 Hz, the period of the AC current is T = 20 ms, and the angular frequency is 314 rad/s. For the frequency of f = 60 Hz, the period is T = 16.66 ms, and the angular frequency is 376.8 rad/s. Just to mention that the AC voltage has the same sinusoidal form as AC current, and the equation for it's waveform is same as for the current, of course, the amplitude is different (it will be, Umax).
Picture 2: Mathematical equations for sinusoidal AC current
RMS value of Alternating current
Root mean square or RMS value of alternating current is defined as that value of steady current, which would generate the same amount of heat in a given resistance for a given time, as is done by AC current, when maintained across the same resistance for the same time. The RMS value is also called effective value or virtual value of alternating current. It is represented by Irms or Ieff. On Picture 3 are shown the equation for calculating the RMS value for an arbitrary periodic waveform i(t) with period T, and the RMS values for a sinusoidal waveform, for a triangle waveform centered about zero and for a square waveform centered about zero. RMS value for a sinusoidal AC current is equal to maximum value divided by square root of 2, or Irms = 0.707 x Imax. The factor 0.707 is called the crest factor. The crest factor varies for different waveforms. As we mentioned above, the same equations are valid and for AC voltage, Urms = Ueff = 0.707 x Umax. So, if the effective value of the AC voltage is 220 V, that means that maximum value is 310 V, or the voltage goes from -310 V to + 310 V, or the peak to peak voltage is 620 V.
Picture 3: RMS value for alternating current
In practice, the most common electrical system is the three-phase electrical system. The simplest case of three-phase electrical generation is three separate coils in the generator stator that are physically offset by an angle of 120° to each other. Three current waveforms are produced that are equal in magnitude and 120° out of phase to each other. The phases are usually marked as L1, L2, L3 (or R, S, T). The waveforms of the three-phase voltages are shown on Picture 4 separately, and on Picture 5 all three phases in same diagram.
Picture 4: Waveforms for three-phase AC voltages
Picture 5: Waveforms for three-phase AC voltages (one diagram)
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