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RLC Circuits
Physics 102
Professor Lee Carkner
Lecture 25
Three AC Circuits
DVmax = 10 V, f = 1Hz, R = 10
DVrms = 0.707 DVmax = (0.707)(10) =
R =
Irms = DVrms/R =
Imax = Irms/0.707 =
Phase Shift =
When V = 0, I =
DVmax = 10 V, f = 1Hz, C = 10 F
DVrms = 0.707 DVmax = (0.707)(10) =
XC = 1/(2pfC) = 1/[(2)(p)(1)(10)] =
Irms = DVrms/XC =
Imax = Irms/0.707 =
Phase Shift =
When V = 0, I = I max =
Three AC Circuits
DVmax = 10 V, f = 1Hz, L = 10 H
DVrms = 0.707 DVmax = (0.707)(10) =
XL = 2pfL = (2)(p)(1)(10) =
Irms = DVrms/XL =
Imax = Irms/0.707 =
Phase Shift =
When V = 0, I = I max =
For capacitor, V lags I
For inductor, V leads I
RLC Circuits

Z = (R2 + (XL - XC)2)½
The voltage through any one circuit element
depends only on its value of R, XC or XL
however
RLC Circuit
RLC Phase

The phase angle f can be related to the
vector sum of the voltages

Called the power factor
RLC Phase Shift
Also: tan f = (XL - XC)/R
The arctan of a positive number is positive so:

Inductance dominates
The arctan of a negative number is negative
so:

Capacitance dominates
The arctan of zero is zero so:

Resistor dominates
Frequency Dependence
The properties of an RLC circuit depend not
just on the circuit elements and voltage but
also on the frequency of the generator

Frequency affects inductors and capacitors
exactly backwards

High f means capacitors never build up much
charge and so have little effect
High and Low f
For “normal” 60 Hz household current both
XL and XC can be significant

For high f the inductor acts like a very large
resistor and the capacitor acts like a
resistance-less wire

At low f, the inductor acts like a resistanceless wire and the capacitor acts like a very
large resistor

High and Low Frequency
Today’s PAL
a)
How would you change Vrms, R, C and
w to increase the rms current through a RC
circuit?
b)
How would you change Vrms, R , L and
w to increase the rms current through a RL
circuit?
c)
How would you change Vrms, R , and w
to increase the current through an RLC
circuit?
d)
What specific relationship between L
and C would produce the maximum current
through a RLC circuit?
LC Circuit

The capacitor discharges as a current through the
inductor

This plate then discharges backwards through the
inductor

Like a mass on a swing
LC Resonance
Oscillation Frequency

Since they are connected in parallel they must
each have the same voltage
IXC = IXL
w = 1/(LC)½
This is the natural frequency of the LC circuit
Natural Frequency

Example: a swing

If you push the swing at all different random
times it won’t

If you connect it to an AC generator with the same
frequency it will have a large current
Resonance

Will happen when Z is a minimum

Z = (R2 + (XL - XC)2)½

This will happen when w = 1/(LC)½
Frequencies near the natural one will
produce large current
Impedance and
Resonance
Resonance Frequency
Resistance and Resonance
Note that the current still depends on the
resistance

So at resonance, the capacitor and inductor
cancel out

Peak becomes shorter and also broader

Next Time
Read 22.1-22.4, 22.7
Homework, Ch 21, P 71, Ch 22, P 3, 7, 8