AC circuits

Direct current (DC) circuits involve currentflowing in one direction. In alternating current (AC) circuits,instead of a constant voltage supplied by a battery, the voltage oscillates ina sine wave pattern, varying with time as:V = V₀sin wt
where w is the angular frequencyrelated to the frequency f by:w = 2pf.In a circuit which only involves resistors, the currentand voltage are in phase with each other, which means that the peak voltageis reached at the same instant as peak current. In circuits which havecapacitors and inductors (coils) the phase relationships will be quitedifferent.

A capacitor is a device for storing charge. It turns out that there isa 90° phase difference between the current and voltage, with the currentreaching its peak 90° (1/4 cycle) before the voltage reaches its peak.Put another way, the current leads the voltage by 90° in a purelycapacitive circuit.A capacitor in an AC circuit exhibits a kind of resistance called capacitivereactance, measured in ohms. This depends on the frequencyof the AC voltage, and is given by:X_C = 1 / wC = 1 / 2pfC
where C is the capacitance of the capacitor measured infarads. We can use the capacitive reactance like a resistance (because, really, it isa resistance) in an equation of the form V = IRto get the voltage across the capacitor: V = IX_C.


An inductor is simply a coil of wire (often wrappedaround a piece of ferromagnet). If we look at a circuit composed only ofan 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. Thistime, however, the current lags the voltage by 90°, so it reaches itspeak 1/4 cycle after the voltage peaks.As with the capacitor, this is usually put in terms of the effectiveresistance of the inductor. This effective resistance is known as theinductive reactance. This is given by:X_L = wL = 2pfL
where L is the inductance of the coil (this depends onthe geometry of the coil and whether it has a ferromagnetic core). The unitof inductance is henry.As with capacitive reactance, the voltage across the inductor is given by:V = IX_C.