Connexions module: m0023 1
Circuits with Capacitors and
Inductors
∗
Don Johnson
This work is produced by The Connexions Project and licensed under the
Creative Commons Attribution License
†
Abstract
Introducing when a circuit has capacitors and inductors other than resistors and sources, the impedance
concept will be applied.
vin +
–
R
Cvout
+
–
Figure 1:
A simple
RC
circuit.
Let's consider a circuit having something other than resistors and sources. Because of KVL, we know
that
vin =vR+vout
. The current through the capacitor is given by
i=Cdvout
dt
, and this current equals that
passing through the resistor. Substituting
vR=Ri
into the KVL equation and using the
v-i
relation for the
capacitor, we arrive at
RC dvout
dt +vout =vin
(1)
The input-output relation for circuits involving energy storage elements takes the form of an ordinary
dierential equation, which we must solve to determine what the output voltage is for a given input. In
contrast to resistive circuits, where we obtain an
explicit
input-output relation, we now have an
implicit
relation that requires more work to obtain answers.
At this point, we could learn how to solve dierential equations. Note rst that even nding the dierential
equation relating an output variable to a source is often very tedious. The parallel and series combination
rules that apply to resistors don't directly apply when capacitors and inductors occur. We would have to slog
∗
Version 2.12: Jun 4, 2009 11:34 am GMT-5
†
http://creativecommons.org/licenses/by/1.0
http://cnx.org/content/m0023/2.12/
