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General Physics (PHY 2140)
Lecture 18
 Electricity and Magnetism
Induced voltages and induction
Generators and motors
Self-induction
Chapter 20
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AC Generators
Basic operation of the generator




As the loop rotates, the magnetic
flux through it changes with time
This induces an emf and a
current in the external circuit
The ends of the loop are
connected to slip rings that rotate
with the loop
Connections to the external
circuit are made by stationary
brushed in contact with the slip
rings
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AC generator (cont)
Generalize the result to N loops
E  NBAw sin wt
EMF generated by the AC generator
where we also noticed that A=la
Emax  NBAw is
Note:
reached when wt=90˚ or 270˚ (loop
parallel to the magnetic field)
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DC generator
By a clever change to the rings and brushes
of the ac generator, we can create a dc
generator, that is, a generator where the
polarity of the emf is always positive.
The basic idea is to use a single split ring
instead of two complete rings. The split ring
is arranged so that, just as the emf is about
to change sign from positive to negative, the
brushes cross the gap, and the polarity of
the contacts is switched.
The polarity of the contacts changes in
phase with the polarity of the emf -- the two
changes essentially cancel each other out,
and the emf remains always positive.
The emf still varies sinusoidally during each
half cycle, but every half cycle is a positive
emf.
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Motors
A motor is basically a generator running in reverse. A
current is passed through the coil, producing a torque
and causing the coil to rotate in the magnetic field. Once
turning, the coil of the motor generates a back emf, just
as does the coil of a generator. The back emf cancels
some of the applied emf, and limits the current through
the coil.
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Motors and Back emf
The phrase back emf is used
for an emf that tends to reduce
the applied current
When a motor is turned on,
there is no back emf initially
The current is very large
because it is limited only by
the resistance of the coil
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20.7 Self-inductance
When a current flows through a loop, the magnetic field
created by that current has a magnetic flux through the
area of the loop.
If the current changes, the magnetic field changes, and
so the flux changes giving rise to an induced emf. This
phenomenon is called self-induction because it si the
loop's own current, and not an external one, that gives
rise to the induced emf.
Faraday’s law states

E  N
t
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The magnetic flux is proportional to the magnetic field,
which is proportional to the current in the circuit
Thus, the self-induced EMF must be proportional to the
time rate of change of the current
I
E  L
t
where L is called the inductance of the device
Units: SI: henry (H)
If flux is initially zero,
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1 H  1V  s
A
 N 
LN

I
I
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Example: solenoid
A solenoid of radius 2.5cm has 400 turns and a length of 20 cm. Find
(a) its inductance and (b) the rate at which current must change
through it to produce an emf of 75mV.
I
E  L
t
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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
1 2
PEL  LI
2
Summary of the properties of circuit elements.
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Resistor
Capacitor
Inductor
units
ohm, W = V / A
farad, F = C / V
henry, H = V s / A
symbol
R
C
L
relation
V=IR
Q=CV
emf = -L (I / t)
power dissipated
P = I V = I² R = V² /
R
0
0
energy stored
0
PEC = C V² / 2
PEL = L I² / 2
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