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PHY 2049: Physics II
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PHY 2049: Physics II
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About bicycle riding: If some one shows
you a trick, it means that,
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It is possible to do that trick
The person who showed you, can do the trick.
It does not mean that you can do the trick.
Try it a lot of times and you can too.
PHY 2049: Physics II
Recall:
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Faraday’s law
Lenz’ law:
the kickback
 B   B.dA
V   E.dl
 B
V  
t
PHY 2049: Physics II
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Recall more
Inductors and inductance
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RL circuits
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Emf induced in a coil when the current changes
Solenoids L = μ0n2lA
I = (1-e-t/τ)V/R
τ = L/R
Energy in a magnetic field
U = ½ Li2, u = B2/2μo
In a coaxial cable the surface is most stressed.
PHY 2049: Physics II
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Mutual induction
E2 = -M21 di1 /dt
M21 = M12
Coil in a coil
M
o N1 N 2 R2 2
2R1
PHY 2049: Physics II
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Three circuit elements:
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Capacitor
Resistor
Inductor
V = Q/C
V = IR
I = dQ/dt
V =- LdI/dt
A general circuit is a combination of these
elements. The analysis is a bit subtle.
PHY 2049: Physics II
PHY 2049: Physics II
a. Long after the switch is closed
In each case the current through R is shorted by the
inductor. The inductor carries all of the current.
b. Switch is opened. The equivalent resistances are (1) R (2)
2R and (3) R/2. Hence by current, the ranking is 3 1 2.
c. Long after the switch is opened, there is no current
anywhere.
PHY 2049: Physics II
PHY 2049: Physics II
Problem 32: The area is v2t2, you can convince
yourself that the two sides of the triangle are
each 2vt/√2. Area A = ½ (2vt/√2)2
At t= 3 s.
Flux = BA = 0.35x 5.22 x32 = 85.2 Wb
Emf around: 56.8 V
Emf = 18.93t., n = 1
PHY 2049: Physics II
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L1
L2
L3
L4
=
=
=
=
30
50
20
15
mH
mH
mH
mH
PHY 2049: Physics II
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L1
L2
L3
L4
=
=
=
=
30
50
20
15
mH
mH
mH
mH
L23 = 14.3
Leq = 30 +15 + 14.3 = 59.3 mH
PHY 2049: Physics II
PHY 2049: Physics II
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E =Ldi/dt
i = Et/L
t = iL/E = 1.5s
PHY 2049: Physics II
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LC oscillations
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For a spring
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Ld2Q/dt2 +Q/C = =
Md2x/dt2 +kx =0
Solution is x = A cosωt
ω = √(k/m)
Here ω = 1/ √(LC)
When there is a natural
frequency, there is violent
response => resonance
Quantity mech
Mass
m
Spring k
Position x
electronic
L
1/C
Q
PHY 2049: Physics II
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Inductors and
inductance
Currents are slowed
down by Faraday’s
law
Eddy currents
More later