Download self-induction

The Quasistationary
Approximation
Ampere’s Law + Faraday’s Law
time x velocity of light >> size
Application in: electrical engineering, radio, TV, audio, …
Inductance
inductive coupling between
two circuits
0
M
4
dl1  dl 2
  r1  r2
 2  MI 1 1  MI 2
dI1
E2   M
dt
dI 2
E1   M
dt
Example 7.10
Find the mutual inductance.
Mutual inductance?
Self-inductance
dI
E  L
dt
L self-inductance
The change of B induces a
back-emf in the loop that
generates the magnetic field:
self-induction.
Unit: Henry 1H=1Vs/A
Example 7.11
Self-inductance of a toroidal
coil with recangular cross section,
which carries a total of N turns.
The transformer
Long distant line
Distribution within a neighborhood
Pline  RI 2
Puser  VI
Low current and high voltage used.
Example 7.12
Oscillator Circuits
q(t )  qo
C
q
qo

2
e


  do  t
2



 o
2
  2t 
q(t )  qo e t
 o
2
2
q(t )  qo e

t
2
cos(dot )

2
 o
Driven Oscillator
AC
C
Driven oscillator with different
initial conditions.
Resonance
Self-excited circuit
1930
Radio tubes
A shipboard radio, circa 1920. Exposed at the operator’s left are the
inductance coils and capacitor plates of the tuning circuit.
transistors
microchip
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/accircon.html#c1
Multi-loop Circuits
Kirchhoff’s rules:
1. When any closed-circuit loop is traversed, the algebraic sum
of the changes in the potential must be equal to zero.
2. At any junction point in a circuit where the current can divide,
the sum of the currents into the junction must equal the sum of
the currents out of the junction.
DC circuit
Find the currents.
AC circuit
I2
Find the currents.
I3