Transcript A Brief History of Planetary Science

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) = 7.07 V
R = 10 W
Irms = DVrms/R = 0.707 A
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) = 7.07 V
XC = 1/(2pfC) = 1/[(2)(p)(1)(10)] =
Irms = DVrms/XC =
Imax = Irms/0.707 =
Phase Shift = ¼ cycle (-p/2)
When V = 0, I = I max = 625 A
Three AC Circuits
DVmax = 10 V, f = 1Hz, L = 10 H
DVrms = 0.707 DVmax = (0.707)(10) = 7.07 V
XL = 2pfL = (2)(p)(1)(10) =
Irms = DVrms/XL =
Imax = Irms/0.707 =
Phase Shift = ¼ cycle (+p/2)
When V = 0, I = I max = 0.16 A
For capacitor, V lags I
For inductor, V leads I
Solving RLC Circuits

w = 2pf
The frequency determines the degree to which
capacitors and inductors affect the flow of current

XC = 1/(wC)
XL = wL
Current and Power
 We use the reactances to find the impedance, which
can be used in the modified version of Ohm’s law to
find the current from the voltage
Z = (R2 + (XL - XC)2)½
DV = IZ

 We then can find the degree to which the total
voltage is out of phase with the current by finding
the phase angle
 The phase angle is also related to the power
Pav = IrmsVrms cos f
RLC Circuit
Frequency Dependence

XL depends directly on w and XC depends
inversely on w

High f means rapid current change, means strong
magnetic inductance and large back emf
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
LC Circuit
Suppose we connect a charged capacitor to an
inductor with no battery or resistor

The inductor keeps the current flowing until the
other plate of the capacitor becomes charged

This process will cycle over and over

LC Resonance
Oscillation Frequency
The rate at which the charge moves back and
forth depends on the values of L and C
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 with the same frequency as the swing
(e.g., every time it reaches the end) it will go
higher
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
This condition is known as resonance
Will happen when Z is a minimum

Z = (R2 + (XL - XC)2)½
To minimize Z want XL = XC

Frequencies near the natural one will
produce large current
Impedance and
Resonance
Resonance Frequency
Resistance and Resonance

The smallest you can make Z is Z = R

If we change R we do not change the natural
frequency, but we do change the magnitude
of the maximum current
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