Chapter 4 Alternating Current 4.1 Definition and Characteristics • Alternating current is defined as current that periodically changes direction and continuously changes in magnitude. • The effective value or root‐mean‐square (rms) of an alternating current is calculated by comparing it with direct current. The comparison is based on the amount of heat produced by each current under identical conditions. • The equation showing the relationship between maximum and rms values is I eff =
Im
≈ 0.707 I m . This 2
relationship is correct for sinusoidal waveforms only. • The number of cycles occurring per second is the frequency of the current and is measured in a unit called the Hertz. The supply frequency in Thailand is 50 Hz. • Alternating currents in airplane circuit usually have a frequency of 400 Hz. • The phase angle is the difference in degrees of rotation between two alternating currents or voltages, or between a voltage and a current. 1 • The current can be lagging the voltage (for inductance) or leading the voltage (for capacitance) or in phase with the voltage (for resistance). • For an inductor (L), the current passes through it lags the voltage across it. For a capacitor (C), the current passes through it leads the voltage across it. • Inductive reactance X L
= ω L = 2π fL and Capacitive reactance X C =
1
1
. The unit for =
ωC 2π fC
reactance is ohm. 4.2 Impedance • The combination of resistance, inductive reactance and capacitive reactance is called impedance (Z). • If we consider inductive reactance as positive, because inductance causes the voltage to lead the current, and capacitive reactance as negative, because it causes the voltage to lag. Then the total reactance (XT) is X T = X L + (− X C ) . • The impedance is Z =
R 2 + ( X L − X C )2 • Examples • True power (P, unit in W) is the power consumed by the resistance of an ac circuit. Apparent power (S, unit in volt‐ampere or VA) is the power consumed by the entire ac circuit (consisting of R, L and C). • Power factor (PF) is the ratio of true power to apparent power. PF represents the circuit’s efficiency. The value of PF is between 0 and 1. PF can also be calculated by using the cosine of the phase shift angle between the voltage and the current or PF = cos θ . It should be noted that P = S x PF. 4.3 AC and the airplane • AC power is much more flexible than DC power. • Alternating current can be converted to different voltages much more easily than direct current. • DC power required is only a very small percentage of the total electric power consumed in the aircraft. DC power is much more for the backup power. • AC systems do have certain disadvantages such as radiation of an electromagnetic field around each conductor. This field can interfere with communication or navigation systems if not properly controlled. Asst. Prof. Thavatchai Tayjasanant, Ph.D. 2