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Chapter 20Chapter 20
Induced Voltages and Inductance
General Physics
Inductors & RL Circuits
Sections 5–8
General Physics
Generators
Alternating Current (AC) and Direct Current (DC) generators– Converts mechanical energy to electrical energy– Consists of a wire loop rotated through a magnetic
field by some external means– There are a variety of sources that can supply the
energy to rotate the loop• These may include falling water, heat by burning coal to
produce steam
General Physics
AC Generators As the loop rotates (θ changes), the
magnetic flux through the loop changes with time
This induces an emf and a current in the external circuit (toaster)
The ends of the loop are connected to slip rings that rotate with the loop
Connections to the external circuit are made by stationary brushes in contact with the slip rings
The output voltage oscillates between positive and negative polarity
The current is an AC current
General Physics
AC Generators – Rotating Loop Wires BC and AD act as bars moving
vertically through the horizontal magnetic field between the N and S poles.
An emf is generated in wires BC and AD
The total emf produced in these 2 wires is ε = 2 B ℓ v= 2 B ℓ v sin θ
If the loop rotates with a constant angular speed, ω, the emf generated by the rotating loop is ε =2 B ℓ (a / 2) ω sin ωt = B A ω sin ωt
If a coil has N turns, the emf is N times as large ε = N B A ω sin ω t
Active Figure: AC Generator
General Physics
DC Generators Components are essentially the
same as that of an AC generator The major difference is the
contacts to the rotating loop are made by a split ring, or commutator
The output voltage always has the same polarity
The current is a DC pulsing current
Active Figure: DC Generator
General Physics
Motors Motors are devices that
convert electrical energy (through magnetic forces) into mechanical energy– A motor is a generator run
in reverse
A motor can perform useful mechanical work when a shaft connected to its rotating coil is attached to some external device
General Physics
Motors and Back emf
As the motor rotates, the magnetic flux through the loop changes with time
This induces a back emf that tends to reduce the current applied to the motor from the external source
When a motor is first turned on, the current is very large because there is no back emf initially
As the coil begins to rotate, the induced back emf opposes the applied voltage
The current in the coil is reduced The power requirements for starting a motor and for running it
under heavy loads are greater than those for running the motor under average loads
General Physics
Joseph Henry
1797 – 1878 First director of the
Smithsonian First president of the Academy
of Natural Science First to produce an electric
current with a magnetic field Improved the design of the
electro-magnetic and constructed a motor
Discovered self-inductance
General Physics
Self-inductance Self-inductance occurs when the
changing flux through a circuit arises from the circuit itself– When the switch is closed, the
current increases from zero– As the current increases, the
magnetic flux through a loop due to this current also increases
– The increasing flux induces an emf that opposes the change in magnetic flux
– As the magnitude of the current increases, the rate of increase lessens and the induced emf decreases
– This opposing emf results in a gradual increase of the current rather than a sharp increase
General Physics
Self-inductance, cont The self-induced emf is proportional to
the time rate of change of the current
– L is a proportionality constant called the self-inductance of the circuit or device
– The SI unit of self-inductance is the Henry1 H = 1 (V · s) / A
– The negative sign indicates that a changing current induces an emf in opposition to that change – Lenz’s law
IL
t
General Physics
Self-inductance, cont The inductance of a coil depends on
geometric factors You can determine L from the
expression
For a solenoid the inductance is
I
NL B
l
rNL
220
General Physics
Self-Inductance and Lenz’ Law
Consider an increasing current through the inductor
The self-induced emf has a direction so as to oppose the increase in the current
Consider a decreasing current through the inductor
The self-induced emf has an opposite direction so as to oppose the decrease in the current
General Physics
Inductor in a Circuit – RL Circuit When the switch is closed, the current
in the RL circuit increases from zero The increasing current induces an emf
in the inductor that opposes the change in the current
As the magnitude of the current increases, the rate of increase lessens and the self-induced emf decreases
When the current reaches its maximum, the rate of change and the self-induced emf become zero
The time constant, , for an RL circuit is the time required for the current in the circuit to reach 63.2% of its final value
General Physics
RL Circuit, cont
The time constant depends on R and L
The current at any time can be found by
LR
/1 tI eR
Active Figure: An RL Circuit
General Physics
Energy Stored in a Magnetic Field
The emf induced by an inductor prevents a battery from establishing an instantaneous current in a circuit
The battery has to do work to produce a current– This work results in energy being stored by the
inductor in its magnetic field
PEL = ½ L I2
– Note that this result is similar to the expression for the energy stored by a capacitor in its electric field
PEC = ½ C ΔV2