Let's take the following example circuit and
analyze it:
The first step is to
determine the reactances (in ohms) for the inductor and the
capacitor.
The next step is to
express all resistances and reactances in a mathematically
common form: impedance. Remember that an inductive reactance
translates into a positive imaginary impedance (or an
impedance at +90 degrees), while a capacitive reactance
translates into a negative imaginary impedance (impedance at
-90 degrees). Resistance, of course, is still regarded as a
purely "real" impedance (polar angle of 0 degrees):
Now, with all quantities of opposition to electric current
expressed in a common, complex number format (as impedances,
and not as resistances or reactances), they can be handled
in the same way as plain resistances in a DC circuit. This
is an ideal time to draw up an analysis table for this
circuit and insert all the "given" figures (total voltage,
and the impedances of the resistor, inductor, and
capacitor).
Unless otherwise specified, the source voltage will be our
reference for phase shift, and so will be written at an
angle of 0 degrees. Remember that there is no such thing as
an "absolute" angle of phase shift for a voltage or current,
since it's always a quantity relative to another waveform.
Phase angles for impedance, however (like those of the
resistor, inductor, and capacitor), are known absolutely,
because the phase relationships between voltage and current
at each component are absolutely defined.
Notice that I'm assuming a perfectly reactive inductor and
capacitor, with impedance phase angles of exactly +90 and
-90 degrees, respectively. Although real components won't be
perfect in this regard, they should be fairly close. For
simplicity, I'll assume perfectly reactive inductors and
capacitors from now on in my example calculations except
where noted otherwise. |