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 Direct current (DC) circuits involve current flowing in one direction. In alternating current (AC) circuits, instead of a constant voltage supplied by a battery, the voltage oscillates in a sine wave pattern, varying with time as: V = V0sin wt where w is the angular frequency related to the frequency f by: w = 2pf. In a circuit which only involves resistors, the current and voltage are in phase with each other, which means that the 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. A capacitor is a device for storing charge. It turns out that there is a 90° phase difference between the current and voltage, with the current reaching its peak 90° (1/4 cycle) before the voltage reaches its peak. Put another way, the current leads the voltage by 90° in a purely capacitive circuit. A capacitor in an AC circuit exhibits a kind of resistance called capacitive reactance, measured in ohms. This depends on the frequency of the AC voltage, and is given by: XC = 1 / wC = 1 / 2pfC where C is the capacitance of the capacitor measured in farads. We can use the capacitive reactance like a resistance (because, really, it is a resistance) in an equation of the form V = IR to get the voltage across the capacitor: V = IXC. An inductor is simply a coil of wire (often wrapped around a piece of ferromagnet). If we look at a circuit composed only of an inductor and an AC power source, we will again find that there is a 90° phase difference between the voltage and the current in the inductor. This time, however, the current lags the voltage by 90°, so it reaches its peak 1/4 cycle after the voltage peaks. As with the capacitor, this is usually put in terms of the effective resistance of the inductor. This effective resistance is known as the inductive reactance. This is given by: XL = wL = 2pfL where L is the inductance of the coil (this depends on the geometry of the coil and whether it has a ferromagnetic core). The unit of inductance is henry. As with capacitive reactance, the voltage across the inductor is given by: V = IXC.

 August 1999 © 1999, Physics by Demonstrations