rlc circuits physics 102 professor lee carkner lecture 25
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RLC Circuits
Physics 102Professor Lee
CarknerLecture 25
Three AC Circuits Vmax = 10 V, f = 1Hz, R = 10
Vrms = 0.707 Vmax = (0.707)(10) = R = Irms = Vrms/R = Imax = Irms/0.707 = Phase Shift = When V = 0, I =
Vmax = 10 V, f = 1Hz, C = 10 F Vrms = 0.707 Vmax = (0.707)(10) = XC = 1/(2fC) = 1/[(2)()(1)(10)] = Irms = Vrms/XC = Imax = Irms/0.707 = Phase Shift = When V = 0, I = I max =
Three AC Circuits Vmax = 10 V, f = 1Hz, L = 10 H
Vrms = 0.707 Vmax = (0.707)(10) =
XL = 2fL = (2)()(1)(10) =
Irms = Vrms/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 can be related to the vector sum of the voltages
Called the power factor
RLC Phase Shift Also: tan = (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 resistance-less 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
to increase the rms current through a RC circuit?
b) How would you change Vrms, R , L and to increase the rms current through a RL circuit?
c) How would you change Vrms, R , and 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
= 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 = 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