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Unformatted text preview: PHYSICS 222
Introduction to Classical Physics II
Prof. Ruslan Prozorov
Iowa State University
Fall 2011 LECTURE 20
Inductance.
Energy of magnetic field.
RL Circuit mutual inductance PHYS222  Lecture 20  Prof. Ruslan Prozorov  Iowa State University 10 October 2011 2 Induction between two coils Change the current in coil 1 changes the Bflux through coil 2 induces an emf in coil 2 PHYS222  Lecture 20  Prof. Ruslan Prozorov  Iowa State University 10 October 2011 3 PHYS222  Lecture 20  Prof. Ruslan Prozorov  Iowa State University 10 October 2011 4 Mutual inductance
d 21
di1 2 N2 M 21
dt
dt
N 2 21
M 21 i1
M21 mutual inductance
indicates how large is an emf in 2
due to current change in 1
Of course it works both ways: di2 1 M12
dt N1 12
M12 i2 PHYS222  Lecture 20  Prof. Ruslan Prozorov  Iowa State University 10 October 2011 5 Mutual inductance depends on the geometry, orientation and materials
of the coils. It can be shown that M21 M12 M Therefore, we have: di2 1 M
dt di1 2 M
dt N2 21 N1 12
M i1
i2
Units: SI Henry 1 H = 1 Wb/A PHYS222  Lecture 20  Prof. Ruslan Prozorov  Iowa State University 10 October 2011 6 mutual inductance of two solenoids l B2 0 n2i2 12 0 n2i2 R12 flux in solenoid 1 due to
field produced by
solenoid 2 n112 n1 ( 0 n2i2 R12 )
M 0 n1n2 R12
i2
i2
PHYS222  Lecture 20  Prof. Ruslan Prozorov  Iowa State University mutual inductance
per unit length 10 October 2011 7 selfinductance
Ideal coil (no resistance)
If current through coil changes, flux through coil changes in each loop there is an induced
emf loops “in series” emf induced
between two ends of coil Single coil is called an inductor
The effect is called selfinduction PHYS222  Lecture 20  Prof. Ruslan Prozorov  Iowa State University L di
dt N B
L
i 10 October 2011 8 real inductors PHYS222  Lecture 20  Prof. Ruslan Prozorov  Iowa State University 10 October 2011 9 inductors work against di/dt
Inductor always acts to oppose current change. setting up a current in a circuit with an inductor will take some time. used in circuit design to protect against rapid changes of currents or spikes
PHYS222  Lecture 20  Prof. Ruslan Prozorov  Iowa State University 10 October 2011 10 resistors and inductors PHYS222  Lecture 20  Prof. Ruslan Prozorov  Iowa State University 10 October 2011 11 RL circuits: current growth Kirchhoff’s law iR L di
0
dt i t 0 0 Differential equation for i + initial condition i t 0 0 i t (no inductor)
R
PHYS222  Lecture 20  Prof. Ruslan Prozorov  Iowa State University Qualitatively: 10 October 2011 12 di iR L
0
dt i ln R R di
R dt L
i
R R t L R R
ln 1 i t L i R i t R R t
1 e L t 1 e L R If L is large, is large, i.e. current grows slowly.
PHYS222  Lecture 20  Prof. Ruslan Prozorov  Iowa State University 10 October 2011 13 inclass example: RL circuit
You have 1000 Ω resistor and you want to build an LR series circuit that will go
from 0 to 0.9 V0/R in 1 ms once the switch is closed. What value should L have? R L i t R V0 t 1 e 0.9 1 e L
R 1 ms 1 ms ln 0.1 0.43 ms L R 0.43 H PHYS222  Lecture 20  Prof. Ruslan Prozorov  Iowa State University 10 October 2011 14 inductor networks
parallel connection PHYS222  Lecture 20  Prof. Ruslan Prozorov  Iowa State University series connection 10 October 2011 15 inductors store energy After the switch is opened, the inductor drives the current
through the resistor. The energy dissipated in the resistor must have been stored
in the inductor. PHYS222  Lecture 20  Prof. Ruslan Prozorov  Iowa State University 10 October 2011 16 energy stored in an inductor
To establish current (from i = 0 to i = I ): di
V L
dt Voltage across inductor:
(ignoring signs) 1) rate of energy supplied to inductor P Vi Li di
dt 2) increase of energy within inductor dU Pdt Li di
I 3) energy stored within inductor U dU L idi
0 1
U LI 2
2
PHYS222  Lecture 20  Prof. Ruslan Prozorov  Iowa State University 10 October 2011 17 ignition coil
An ignition coil (also called a spark coil) is an
induction coil in an automobile's ignition system
which transforms the battery's 12 volts (6 volts
in some older vehicles) to the thousands of
volts (20 to 30 thousand volts or more) needed
to spark the spark plugs.
This specific form of the autotransformer,
together with the contact breaker and a
capacitor converts low voltage from a battery
into the high voltage required by spark plugs in
an internal combustion engine. PHYS222  Lecture 20  Prof. Ruslan Prozorov  Iowa State University 10 October 2011 18 ...
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