1. General Physics (PHY 2140) Lecture 19 Electricity and Magnetism
Induced voltages and induction
Energy
AC circuits and EM waves
Resistors in an AC circuits
Chapter 20-21
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2. Next week: Prof. Claude Pruneau
Lectures on Monday and Wednesday
Exam on Friday
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3. Lightning Review Last lecture: Induced voltages and induction
Generators and motors
Self-induction
Review Problem: Charged particles passing through a bubble chamber leave tracks consisting of small hydrogen gas bubbles. These bubbles make visible the particles’ trajectories. In the following figure, the magnetic field is directed into the page, and the tracks are in the plane of the page, in the directions indicated by the arrows. (a) Which of the tracks correspond to positively charged particles? (b) If all three particles have the same mass and charges of equal magnitude, which is moving the fastest?
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4. S S N v Review example change
Determine the direction of current in the loop for bar magnet moving down. v N
Initial flux
Final flux
By Lenz’s law, the induced field is this
change
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5. Inductor in a Circuit
Inductance can be interpreted as a measure of opposition to the rate of change in the current
Remember resistance R is a measure of opposition to the current
As a circuit is completed, the current begins to increase, but the inductor produces an emf that opposes the increasing current
Therefore, the current doesn’t change from 0 to its maximum instantaneously
Maximum current:
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6. 20.9 Energy stored in a magnetic field
The battery in any circuit that contains a coil has to do work to produce a current
Similar to the capacitor, any coil (or inductor) would store potential energy
Summary of the properties of circuit elements.
Resistor
Capacitor
Inductor
units
ohm, W = V / A
farad, F = C / V
henry, H = V s / A
symbol R C L
relation
V = I R
Q = C V
emf = -L (DI / Dt)
power dissipated
P = I V = I² R
= V² / R
energy stored
PEC = C V² / 2
PEL = L I² / 2
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7. Example: stored energy
A 24V battery is connected in series with a resistor and an inductor, where R = 8.0W and L = 4.0H. Find the energy stored in the inductor when the current reaches its maximum value.
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8. Recall that the energy stored in th inductor is Given: V = 24 V
A 24V battery is connected in series with a resistor and an inductor, where R = 8.0W and L = 4.0H. Find the energy stored in the inductor when the current reaches its maximum value.
Recall that the energy stored in th inductor is
Given:
V = 24 V
R = 8.0 W
L = 4.0 H
Find:
PEL =?
The only thing that is unknown in the equation above is current. The maximum value for the current is
Inserting this into the above expression for the energy gives
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9. Alternating Current Circuits and Electromagnetic Waves
Chapter 21
Alternating Current Circuits
and Electromagnetic Waves

10. AC Circuit
An AC circuit consists of a combination of circuit elements and an AC generator or source
The output of an AC generator is sinusoidal and varies with time according to the following equation
ΔV = ΔVmax sin 2ƒt
Δv is the instantaneous voltage
ΔVmax is the maximum voltage of the generator
ƒ is the frequency at which the voltage changes, in Hz
Same thing about the current (if only a resistor)
I = Imax sin 2ƒt
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11. Resistor in an AC Circuit
Consider a circuit consisting of an AC source and a resistor
The graph shows the current through and the voltage across the resistor
The current and the voltage reach their maximum values at the same time
The current and the voltage are said to be in phase
Voltage varies as
ΔV = ΔVmax sin 2ƒt
Same thing about the current
I = Imax sin 2ƒt
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12. More About Resistors in an AC Circuit
The direction of the current has no effect on the behavior of the resistor
The rate at which electrical energy is dissipated in the circuit is given by
P = i2 R = (Imax sin 2ƒt)2 R
where i is the instantaneous current
the heating effect produced by an AC current with a maximum value of Imax is not the same as that of a DC current of the same value
The maximum current occurs for a small amount of time
Averaging the above formula over one cycle we get
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13. rms Current and Voltage
The rms current is the direct current that would dissipate the same amount of energy in a resistor as is actually dissipated by the AC current
Alternating voltages can also be discussed in terms of rms values
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14. Ohm’s Law in an AC Circuit
rms values will be used when discussing AC currents and voltages
AC ammeters and voltmeters are designed to read rms values
Many of the equations will be in the same form as in DC circuits
Ohm’s Law for a resistor, R, in an AC circuit
ΔVrms = Irms R
Also applies to the maximum values of v and i
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15. Example: an AC circuit
An ac voltage source has an output of DV = 150 sin (377 t). Find
(a) the rms voltage output,
(b) the frequency of the source, and
(c) the voltage at t = (1/120)s.
(d) Find the maximum current in the circuit when the generator is connected to a 50.0W resistor.
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16. Capacitors in an AC Circuit
Consider a circuit containing a capacitor and an AC source
The current starts out at a large value and charges the plates of the capacitor
There is initially no resistance to hinder the flow of the current while the plates are not charged
As the charge on the plates increases, the voltage across the plates increases and the current flowing in the circuit decreases
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17. More About Capacitors in an AC Circuit
The current reverses direction
The voltage across the plates decreases as the plates lose the charge they had accumulated
The voltage across the capacitor lags behind the current by 90°
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18. Capacitive Reactance and Ohm’s Law
The impeding effect of a capacitor on the current in an AC circuit is called the capacitive reactance and is given by
When ƒ is in Hz and C is in F, XC will be in ohms
Ohm’s Law for a capacitor in an AC circuit
ΔVrms = Irms XC
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19. Inductors in an AC Circuit
Consider an AC circuit with a source and an inductor
The current in the circuit is impeded by the back emf of the inductor
The voltage across the inductor always leads the current by 90°
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20. Inductive Reactance and Ohm’s Law
The effective resistance of a coil in an AC circuit is called its inductive reactance and is given by
XL = 2ƒL
When ƒ is in Hz and L is in H, XL will be in ohms
Ohm’s Law for the inductor
ΔVrms = Irms XL
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21. Example: AC circuit with capacitors and inductors
A 2.40mF capacitor is connected across an alternating voltage with an rms value of 9.00V. The rms current in the capacitor is 25.0mA. (a) What is the source frequency? (b) If the capacitor is replaced by an ideal coil with an inductance of 0.160H, what is the rms current in the coil?
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