,max
max
source
V
I
Z
(Eq. 3)
These strange, but necessary, quantities (phase difference and impedance) for modeling the
behavior of an AC circuit arise from the behavior of two particular circuit elements – the
capacitor and the inductor.
You may have encountered a capacitor in the lab activity, “DC Electric Circuits – The RC
Circuit.” A capacitor is constructed from separate conducting surfaces that are able to store equal
and opposite amounts of electric charge. In a DC electric circuit with a capacitor and resistor
connected to a power source, the capacitor would charge, eventually causing the current in the
circuit to become zero, as the potential difference across the capacitor would eventually equal the
potential difference of the source. But, in an AC circuit, where the potential difference of the
source is oscillating in time, the electric charge on the plates and the potential difference across
the capacitor must also oscillate with time. The competing potential differences from the power
source and that building up on the capacitor cause an effect where the maximum potential
difference across the capacitor and the source lag the behavior of the current. Thus, if only a
capacitor and resistor were connected to an AC source, we would expect the maximum value of
the current to occur before the maximum value of the potential difference across the source to
occur.
An inductor is constructed from a coil of wire that will store energy in a magnetic field created
within the inducting coil, because of the current running through it. In a DC electric circuit with
an inductor and resistor connected to a power source, the inductor would initially create a back
current, due to Faraday’s Law, that would cause the circuit to take more time to reach the
maximum current than expected. Eventually, there is no back current created by the inductor,
once the current in the inductor reaches its maximum value, and becomes constant. In an AC
circuit, where the potential difference of the source is oscillating in time, the current is almost
always changing, resulting in a back current almost always being created in the circuit, due to the
inductor. This would result in a scenario where the potential difference across the inductor and
the source lead the behavior of the current. Thus, if only an inductor and resistor were connected
to an AC source, we would expect the maximum value of the current to occur after the maximum
value of the potential difference across the source to occur.
Given the behaviors described for the capacitor and the inductor in an AC circuit, we can
imagine that we might think of each circuit element as having some kind of resistive effect on
the circuit. These resistive effects, or
reactances
, depend on the frequency of oscillation of the
power source, and thus the current through the circuit elements. The resistive effect of the
capacitor in an AC circuit is called the
capacitive reactance
, and the resistive effect of the
inductor in an AC circuit is called the
inductive reactance
. These two reactances are given by Eq.
4 and 5 below, where both are measured in the SI unit of ohms,
.