Home > Textbooks > Lessons In Electric Circuits > Vol. II - AC > Reactance and Impedance - R, L, and C > Review of R, X, and Z

Chapter 5: REACTANCE AND IMPEDANCE - R, L, AND C

# 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 (Figure below) possess resistance, but not reactance. Perfect inductors and perfect capacitors (Figure below) 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.

*Perfect resistor, inductor, and capacitor.*

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!

## Related Content:

Video lecture: AC Circuits Basics, Impedance, Resonant Frequency, RL RC RLC LC Circuit Explained, Physics Problems