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The Quasistationary Approximation
Ampere’s Law + Faraday’s Law
Application in: electrical engineering, radio, TV, audio, …
time x velocity of light >> size
Inductance
inductive coupling betweentwo circuits
dt
dIM
dt
dIM
MIMI
ddM
21
12
2112
21
210
4
EE
rr
ll
Example 7.10
Find the mutual inductance.
Mutual inductance?
Self-inductance
The change of B induces a back-emf in the loop that generates the magnetic field:self-induction.
dt
dILE
L self-inductance
Unit: Henry 1H=1Vs/A
Example 7.11
Self-inductance of a toroidalcoil with recangular cross section,which carries a total of N turns.
The transformer
VIP
RIP
user
line
2
Low current and high voltage used.
Long distant line Distribution within a neighborhood
Example 7.12
oq
q
Oscillator Circuits
C
o
t
o teqtq
22)( 2
o
t
o
do
eqtq
22)( 2
odo
t
o teqtq
2)cos()( 2
Driven Oscillator
C
AC
Driven oscillator with differentinitial conditions.
Resonance
Self-excited circuit
Radio tubes
1930
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.
Find the currents.
AC circuit
3I2I
