In the circuits at right, we
include a "generator" whose voltage varies as V0sinωDt,
where ωD is the so-called driving frequency.
Applying the loop theorem to this circuit gives
Note that the maximum charge, qm, and maximum current, im, are functions of the driving frequency ωD and the "natural" frequency of the circuit, ω ( = 1/√(LC),
This
function has its maximum value when ωD =
ω. In this case the circuit is in RESONANCE. The diagram at right shows the
current in the circuit as a function of ωD
for several different values of R. [ In
this picture ω = ωD
and ω0 = ω ] The maximumu
(resonant) current in the circuit increases as R
decreases.The phenomenon of resonance in LCR circuits is used to obtain a maximum signal when tuning radios, TVs etc to a particular frequency. In this situation ωD is the fixed frequency of the transmitted signal and the natural frequency of the tuning circuit (ω) is adjusted, typically by means of a variable capacitor, to obtain maximum amplitude current (which translates to maximum signal volume).
There is a one-to-one correspondence
between mechanical and electrical oscillations and
resonance. The mathematical analysis is
identical. If you followed the description of
oscillations in Physics 298 you should find this
discussion relatively straightforward. Famous Physicists at a party : Ohm spent most of the time resisting Ampere's opinions on current events.
Dr. C. L. Davis
Physics Department
University of Louisville
email: c.l.davis@louisville.edu
