__Review of R, X, and Z__
Before we begin to explore the effects of
resistors, inductors, and capacitors connected together in
the same AC circuits, let's briefly review some basic terms
and facts.
**Resistance** is essentially *friction*
against the motion of electrons. It is present in all
conductors to some extent (except *super*conductors!),
most notably in resistors. When alternating current goes
through a resistance, a voltage drop is produced that is
in-phase with the current. Resistance is mathematically
symbolized by the letter "R" and is measured in the unit of
ohms (Ω).
**Reactance** is essentially *inertia*
against the motion of electrons. It is present anywhere
electric or magnetic fields are developed in proportion to
applied voltage or current, respectively; but most notably
in capacitors and inductors. When alternating current goes
through a pure reactance, a voltage drop is produced that is
90^{o} out of phase with the current. Reactance is
mathematically symbolized by the letter "X" and is measured
in the unit of ohms (Ω).
**Impedance** is a comprehensive
expression of any and all forms of opposition to electron
flow, including both resistance and reactance. It is present
in all circuits, and in all components. When alternating
current goes through an impedance, a voltage drop is
produced that is somewhere between 0^{o} and 90^{o}
out of phase with the current. Impedance is mathematically
symbolized by the letter "Z" and is measured in the unit of
ohms (Ω), in complex form.
Perfect resistors possess resistance, but
not reactance. Perfect inductors and perfect capacitors
possess reactance but no resistance. All components possess
impedance, and because of this universal quality, it makes
sense to translate all component values (resistance,
inductance, capacitance) into common terms of impedance as
the first step in analyzing an AC circuit.
The impedance phase angle for any component
is the phase shift between voltage across that component and
current through that component. For a perfect resistor, the
voltage drop and current are *always* in phase with
each other, and so the impedance angle of a resistor is said
to be 0^{o}. For an perfect inductor, voltage drop
always leads current by 90^{o}, and so an inductor's
impedance phase angle is said to be +90^{o}. For a
perfect capacitor, voltage drop always lags current by 90^{o},
and so a capacitor's impedance phase angle is said to be -90^{o}.
Impedances in AC behave analogously to
resistances in DC circuits: they add in series, and they
diminish in parallel. A revised version of Ohm's Law, based
on impedance rather than resistance, looks like this:
Kirchhoff's Laws and all network analysis
methods and theorems are true for AC circuits as well, so
long as quantities are represented in complex rather than
scalar form. While this qualified equivalence may be
arithmetically challenging, it is conceptually simple and
elegant. The only real difference between DC and AC circuit
calculations is in regard to *power*. Because reactance
doesn't dissipate power as resistance does, the concept of
power in AC circuits is radically different from that of DC
circuits. More on this subject in a later chapter! |