20.4 Self inductance

1
20.4 Self inductance

• Self inductance
• RL circuit

2
We learned that a changing magnetic field in coil
a produces an emf in coil b
b
a
e
However changing fields in coil a due to
changing the current in coil a itself also
produce an emf in coil a. This is called the
self inductance. Inductance is present in any
circuit. However, special circuit elements
called inductors are often used in electronic
circuits.
e
3
Self-inductance of a coil
B increases,
B
changes magnetic flux in the coil,
I
Current increasing
Produces emf in coil
The direction of the induced emf opposes the
change in current.
4
A changing current in a coil induces an emf that
opposes the change

-
e

-
e
I increasing
I decreasing
5
Inductance L is a measure of the self-induced emf
The self-induced emf is
e
but
therefore
Current increasing
proportionality constant is L
L is a property of the coil, Units of L , Henry
(H)
6
Inductance of a solenoid with N turns and length
l, wound around an air core (assume the length is
much larger than the diameter).
7
Change in L?
L increase
L increase
L increase
8
An air wound solenoid of 100 turns has a length
of 10 cm and a diameter of 1 cm. Find the
inductance of the coil.
l 10 cm
d1 cm
9
A solenoid with L1x10-4 H is in a circuit and
experiences a change in current from 0 to 10 A in
1.0 ms. Find the self-induced emf in the
solenoid
The emf opposes the current direction
10
RL Circuits
Inductor
The voltage across an inductor depends the rate
of change of the current. The inductance acts to
maintain a constant current i.e. sort of current
inertia
11
Time for current to increase from I0 to I
At any time Kirchoffs rule
?Vs?VR?VL0
Just after the switch is closed I0,
After the switch is closed for a long time I
constant
12
Time constant
long time
0.63Imax
short time
I
?
time
0
exact solution
the larger L, longer time to reach max current
13
46. For the following circuit, ?Vs6.0 V, L 8.0
mH, and R4.0 O, a) What is the inductive time
constant? b) what is the current 250µs after the
switch is closed?c) What is the value of the
steady state current? d) How long does it take
to reach 80 of its maximum value?
a)
b)
c)
14
46. For the following circuit, ?Vs6.0 V, L 8.0
mH, and R4.0 O, a) What is the inductive time
constant? b) what is the current 250µs after the
switch is closed?c) What is the value of the
steady state current? d) How long does it take
to reach 80 of its maximum value?
d)
15
Back emf
Voltage produced by decreasing current
e is very high (1000 V) if switch is opened
quickly. Unplugging your vacuum cleaner can
cause spark across the plug. Spark plugs in
cars use this
?Vs
L
I decreasing
Switch