Transcript Induction Applications

Lecture 10
Induction Applications
Chapter 20.6  20.8
Outline
• Self-Inductance
• RL Circuits
• Energy Stored in a Magnetic Field
Self-Inductance
I
B
R
Faraday’s law prevents the current in a circuit to reach the
maximum value immediately.
The magnetic flux through the loop increases together
with the current.
As a result, an induced emf appears and opposes the
change in magnetic flux.
The opposing emf results in a gradual increase of the
current.
The effect is called self-inductance.
Magnitude of Self-Inductance
ℇ =  N B/t
The self-induced emf is proportional to the time
rate of change of the current.
I
ℇ = L 
t
L is called inductance
The SI unit of inductance is henry
1H=1Vs/A
N B/t = L I / t
 L = N B/I = N B/I
RL Circuits
Solenoids or closely wrapped coils have a large
inductance and are called inductors.
For a circuits with a resistor ℇ  IR = 0 and V= IR.
Resistance is a measure of opposition to the current.
Inductance is a measure of opposition to the rate of
change in current (ℇ =  L I / t).
For a circuit with both a resistor and an inductor, the
current is unable to reach its maximum value
instantaneously. We can define a time constant for
such a circuit as  = L/R.
Problem with an RL Circuit
Problem: A circuit has a 10-V battery, a 5-
resistor, and a 20-mH inductor.
Find the circuit time constant and the current
after 1 time constant.
 = L/R = 20 102 H / 5  = 0.04 s
I = ℇ/R (1  eRt/L)
t =   1  e1 = 0.632
I = 0.632 ℇ/R = 0.632 10 V / 5  = 1.26 A
Energy Stored in a Magnetic Field
The battery has to do work to produce a current.
This work is energy stored by the inductor in its
magnetic field.
The energy stored by an inductor is similar to that
of a capacitor.
C V2
PEC = 
2
L I2
PEL = 
2
Summary
• Self-inductance is a phenomenon of opposing to
a change in current in electric circuits due to
appearance of the magnetic field.
• Inductor is an element with a large inductance.
• Energy stored by an inductor is similar to that
stored by a capacitor.