318 Week 9: Alternating Current Circuits
problems has you do this very thing. Be sure that you work throughit, with the help of your
instructor as necessary.
So much for the generation and efficient transmission of power, which we can see relies very
much on AC currents and generators. Next we move on to the use of alternating voltages ofmuch
higher frequency, frequencies that we can associated with radio waves and information processing.
The electrical circuits that allow us to generate, transmit, receive, encode and decode information
in alternating flows of current are very nearly as important to modern society as the direct delivery
of electrical power in the first place. They are also useful in the laboratory, and are key components
of much medical apparatus, information technology apparatus, entertainment apparatus – they
are ubiquitous, in other words. We begin by seeing how simple arrangements of resistances and
inductances canoscillatein a way that ismathematically identicalto the way a mass on a spring
oscillates.
9.2: AC Circuits
To make this section as simple as possible, we begin by noting that in thecontext of Kirchoff’s rules
and electrical circuits, a capacitor playspreciselythe same role as a spring does in mechanics – it
stores electrical charge and energy with a restoring “force” proportional to the charge. A resistance
behavesexactlylike a linear drag force does on the mechanical movement of the stored charge. An
inductance behavesexactlylike a mass does in a spring-driven harmonic oscillator, as a reservoir for
the “kinetic” energy associated with flowing charge and the “momentum” that causes that charge
to tend to continue flowing unless acted on by opposing forces. Finally, a harmonically alternating
voltage behavesexactlylike a harmonically altering driving force in the damped, driven harmonic
oscillator.
One can also build a circuit made entirely out ofwater-filled pipesthat precisely mimics an
electrical circuit. A section of the pipe containing a spring loaded piston that can store water on
one side against the pressure difference maintained by the spring is a“capacitor”. A sand-filled
pipe that resists the flow of water is a “resistor”. The water itself,which is massive and hence
continues to flow in the (frictionless) pipe until slowed down by resistances or pressure differences
is an “inductor”. Finally, a pump that creates a harmonically oscillatingpressure difference in the
water, e.g. a harmonically driven pistor in a pipe, is just like an “alternating voltage”.
Keep this in mind as we develop the following. Even though of course the algebra will be specific
to the particular circuits being studied, the results will beanalogousto identical results that arise
from solving identical equations in other contexts you have alreadyexplored in mechanics. This
conceptual repitition can help you learn the material more easily, and help you remember it for
longer without additional reinforcement, provided (of course) that you properly studied harmonic
oscillators thefirsttime you encountered them.
Non-driven LC circuit
+Q
C
S
L
Figure 121: UndrivenLCcircuit