BELIEVE   ME   NOT!    - -     A   SKEPTIC's   GUIDE  

AC RC CIRCUITS

The term "AC" stands for "Alternating Current", typically the 60 Hz power available from any North American electrical outlet.^21.1 A complete discussion of AC circuits must involve the "inertial" effect of inductance, but a useful introduction can be developed using only capacitance $C$ and resistance $R$.

We begin by picturing a generic series-$RC$ circuit driven by a sinusoidal voltage ${\cal E}(t) = {\cal E}_0 \cos (\omega t) = \Re \; e^{i \omega t}$. It is convenient to use the complex form^21.2for calculations; just remember that none of the actual physical quantities like current or voltage will actually have a measurable imaginary part.^21.3 The voltage amplitude ${\cal E}_0$ is taken to be pure real.

Figure:  An $RC$ circuit driven by an AC voltage.

Footnotes

. . . outlet.^21.1

In Europe and much of Asia the standard is 50 Hz.

. . . form^21.2

Here $\Re$ signifies "the real part of" a complex quantity like $e^{i \theta} = \cos \theta + i \sin \theta$. The imaginary part is written (e.g.) $\Im \; e^{i \theta} = \sin \theta$.

. . . part.^21.3

Let me know if you invent an imaginary voltmeter!