Transcript Self Inductance.

Inductors
Toroidal core
An inductor is a wire coil usually wrapped
around an iron core
Self Inductance
A coil can induce a voltage in itself !!!??
Predict what happens when the switch
closes.
What happens when the switch opens?
An inductor is designed to oppose a
changing current
This is because it can induce an EMF in
itself. This is called Self Inductance.
Increasing current
Current Increasing
Causes increasing magnetic field
Causes increasing flux through coil
Causes induced EMF
Increasing current
Direction of EMF
opposes current change
Induced EMF
Self Inductance
• A coil can induce a voltage in itself.

LI
EMF in coil  

t
t
• L is called the self inductance
Self Inductance (L) is measured in henries (H)
Circuit Symbol for inductor:
Considering resistance:
• This induced EMF (or back EMF) opposes
the increase in current, so the current
rises…
SLOWLY
This is called Self Inductance
(The coil induces an EMF in itself)
current
I = V/R
R is the ohmic resistance
of the inductor
L

R
Close switch
time
current
Close switch
LI
EMF in coil  
t
Back
EMF
Close switch
Imax
0.63 Imax
Close
switch
L

R

time
Meaning of time constant :
The time taken for the current to increase to 63% of
the maximum value.
L

R
Larger inductance produces
larger back EMF with the same
change rate of magnetic flux as
Δφ
in ε  L Δt . It opposes the EMF
of the power supply, resulting in
longer time to reach maximum
current.
Larger resistance results in smaller
maximum current. So it takes shorter
time to reach 63% of the maximum
current, resulting in smaller τ.
How would the graph change if:
Inductor had higher inductance?
Inductor had higher resistance (be careful)
current
Close switch
Time
Decreasing current
Current Decreasing
Causes decreasing magnetic field
flux decreasing
Causes induced EMF
Direction of EMF
opposes current change.
This induced EMF (or back EMF)
opposes the decrease in current, so
the current drops…
SLOWLY
This is called Self Inductance
Key idea:
• Inductors oppose a changing current
but have no effect on constant current.
• n.b. a real inductor has resistance
When the switch opens, the current drops to
zero rapidly
Causes a large flux change rate
Induces a very large EMF
Causes a spark across the switch
Energy stored in an inductor
Current in an inductor produces a magnetic
field, therefore energy is stored in the
magnetic field.
1 2
E  LI
2
L: self inductance in henries (H),
I: current in amps (A)
• Inductor radio
Example: As shown, the coil
has an inductance of 0.20H.
When the switch S is open,
the current falls from 5.0A
to zero in 1.0s.
a. What is the induced voltage?
b. What is the resistance, R, of the coil
c. What is the energy stored when S is
closed?
d. What is the time constant of the coil?
L  0.20H, t  1.0s, V  3.0V, Io  5.0 A
LI 0.20  5.0
a. V  

 1.0V
t
1.0
V 3.0
b. R 

 0.60Ω
I
5.0
1 2 1
c. E  LI   0.20  5.0 2  2.5J
2
2
L 0.20
d.  

 0.33s
R 0.60
Ex. (a) What is the steady current flowing when the
switch has been closed for a long time?
(b). What is the voltage across the
inductor at the instant the witch is
closed?
(c) find the time constant.
(d)How long does it take for the
current to reach a value of 0.021A?
Mutual Inductance
http://phet.colorado.edu/webpages/simulations-base.html