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
XC = 1 / wC = 1 / 2pfC
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
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:
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.