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 superconductors!), 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 90o 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 0o and 90o
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 0o. For an perfect
inductor, voltage drop always leads current by 90o, and so an
inductor's impedance phase angle is said to be +90o. For a
perfect capacitor, voltage drop always lags current by 90o,
and so a capacitor's impedance phase angle is said to be -90o.
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!
|
