Download Induced Voltage and Inductance

Induced Voltage and Inductance
• When the switch is closed it causes a temporary
current to flow in the secondary coil. Opening the
switch again causes a current to flow. Ammeter
Switch
Iron Ring
+
Battery
A
Primary Coil
Secondary Coil
Induced emf
• When the current flows in the primary coil a
magnetic field is produced. This in turn causes a
temporary current to flow in the secondary coil.
The ammeter reads only for a brief time and
then returns to zero.
• When the switch is opened the ammeter reads a
current in the opposite direction for a brief
moment, indicating a magnetic field in the
opposite direction. The magnetic field must
keep changing to produce a current
Magnetic Flux
• An electric current can also be created if a
loop conductor is rotated in the presents of a
stationary magnetic field. ( a generator)
• Magnetic flux is a measure of how much
magnetic field influences a surface.
• Magnetic Flux
B = BA cos ( webers)
where B = magnetic field A = area of loop
 = the angle field makes to the normal of the
area If B is perpendicular to A  = 0o
Faraday’s Law of Induction
• If a loop is moved toward or away from a
stationary magnetic field, or a magnet is
moved towards or away from a stationary loop
an electric current will be produced. This
relative motion produces an induced current.
Faraday’s Law of magnetic induction states
that the induced emf E =-N(B)/t
• where N is the number of turns in the loop.
Cont.
• Because B = BA cos any change in B A or
 with time produces an emf. The minus sign
indicates (polarity) the two different
directions the current flows in the loop.
Motional emf
• Motional emf is the emf induced in a
conductor as it moves through a magnetic
field. Thus changing a loop’s area induces a
current in a closed circuit.
Current
B
Magnet field
into the page
R
x
Sliding bar
The sliding bar
moves trough x
increasing A of
the loop
l
l is the length
of the moving bar
Cont.
• For the above diagram as the bar moves
through x in time t, the increase in flux in
that time is the amount of flux that passes
through lx that is B = BA = Blx
• therefore E = B/t =Bl(x/t) = Blv
• As E = IR = (Blv)/R
Lenz’s Law
• Lenz’s law states that the direction of the
induced emf is such that if an induced current
were able to flow, it oppose the change that
causes it.
• In the above diagram as the bar moves to the
right the flux is increased into the page. To
offset this the induced current must flow
counterclockwise.If the bar is moved to the
left current would flow clockwise. Induced
current tends to maintain the original flux.
AC Generators
• An alternating current generator is a device
that turns mechanical energy into electrical
energy. It consists of a wire loop that is rotated
in a magnetic field.
• Consider a loop of area A with N number of
loops in a magnetic field of B moving at an
angular speed of  then E=NBA sin t
when t = 90o or 270o then E= Emax=NBA 
DC Generator
• DC generators are essentially the same as
AC generators except that contact with the
rotating loops are made with split rings so
as to produce a changing magnetic field
which allows for continual rotation.
Motors and back emf
• A motor is basically a generator in reverse.
That is a current is supplied to a loop by an
emf source and the magnetic torque on the
loop causes it to rotate.
• As the loop rotates changing magnetic flux
induces an emf which reduces the current in
the loop, (lenz’s law). Back emf is this
reduced current which reduces the overall
emf.
Cont.
• When a loop starts to rotate there is no back
emf. However after maximum rotation is
achieved back emf is established
• Supplied emf is Esupplied = E- Eback
• When the motor starts initially with no back
emf the current is large. As the loop rotates
back emf opposes the applied voltage and the
current is reduced.
Self Inductance
• Consider a circuit with a switch, a resistor
and an emf source. When the switch is
initially closed the current is not at
maximum, it takes time to build, as does the
magnetic flux in the loop. The increasing
flux in the loop produces an induced emf
that opposes the source emf, (Lenz’s Law).
• The net emf across the resistor is the emf of
Cont.
The battery minus the induced emf.
• This opposing emf results in a gradual
increases in current. As the magnitude of the
current increases the opposing emf decreases.
• The same occurs when the switch is opened,
the current does not immediately fall to zero.
• This effect is called self induction because the
changing flux through the circuit is caused by
the circuit.
Cont.
• The emf that is set up in a circuit by the
circuit is called self-induced emf and is
given by emf = Δv = -LΔI/Δt
where L is a proportionality constant called
inductance of the device. The negative sign
indicates that the changing current induces
an emf in opposition to the change.
Cont.
• The SI unit for inductance is a Henry (H)
1 H = 1 V.s/A
As emf = -N(B)/t = -LΔI/Δt
then L = (N B)/I
For a solenoid of cross-sectional area A and length l
L=( µoN2A)/l = µon2V
Where n = number of turns per unit length
V = volume of solenoid
RL Circuits
• Resistance is a measure of opposition to the
current
• Inductance is a measure of the opposition to
the rate of current change.
• The time constant of a circuit is the time
required for the current in a circuit to reach
63.2% of its final value of I τ = L/R
Energy Stored in a Magnetic Field
• Inductor induced emf prevents a battery
from establishing instantaneous current. The
battery must do work to establish current as
equating it to energy stored in the inductor
• PEL = ½ LI2