Transcript PowerPoint 簡報 - Happy Physics
Physics Lecture Resources
Prof. Mineesh Gulati Head-Physics Wing Happy Model Hr. Sec. School, Udhampur, J&K Website: happyphysics.com
happyphysics.com
Ch 30 Inductance
© 2005 Pearson Education
30.1 Mutual Inductance
mutually induced emfs
ε
2
M di
1
dt
and
ε
1
M di
2
dt
mutual inductance
M
N
2
B
2
i
1
N
1
B
1
i
2 © 2005 Pearson Education
Unit :henry (H)
Application of Mutual Inductance
© 2005 Pearson Education
Example 30.1
In one form of Tesla coil, a long solenoid with length l and cross-sectional area A is closely wound with N 1 turns of wire. A coil with N 2 turns surrounds it at its center. Find the mutual inductance.
ANS:
B
1 0
n i
1 1 0
N i
1 1
l M
N
2
B
2
i
1
N B A
2 1
N
2
i
1 0
N i
1 1
l
0
AN N
1 2
A l
© 2005 Pearson Education
30.2 Self-Inductors
Current I ->B-field ->flux ->I change ->flux change ->self-induced emf appears self-induced emf
ε
di L dt
self-inductance
L
N
B i
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Circuit symbol For inductor
© 2005 Pearson Education
© 2005 Pearson Education
Example 30.3
Determine the self-inductance L of toroidal solenoid
ANS:
B BA
L
N
B i
0 2
N A
2
r
NiA
0 2
r
© 2005 Pearson Education
30.3 Magnetic-Field Energy
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energy stored in an inductor
U
L
0
I i di
1 2
LI
2
magnetic energy density in a vacuum
u
B
2 2 0
magnetic energy density in a material
u
B
2 2 © 2005 Pearson Education
30.4 The R-L Circuit
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Growth of current in R-L circuit
time constant for an R-L circuit
L R
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Decay of current in an R-L circuit
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30.5 The
L
-
C
Circuit
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© 2005 Pearson Education
angular frequency of oscillation in an L-C circuit
ω
1
LC
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30.6 The
L
-
R
-
C
Series Circuit
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underdamped L-R- C series circuit
ω
1
LC
R
2 4
L
2 © 2005 Pearson Education
When a changing current i 1 in one circuit causes a changing magnetic flux in a second circuit, an emf ε 1 is induced in the second circuit. Likewise, a charging current i 2 in the second circuit induces an emf ε 2 in the first circuit. The mutual inductance M depends on the geometry of the two coils and the material between them. If the circuits are coils of wire with N 1 and N 2 turns, respectively, M can be expressed in terms of the average flux Φ B2 through each turn of coil 2 that is caused by the current i 1 in coil 1, or in terms of the average flux Φ B1 through each turn of coil 1 that is caused by the current i 2 in coil 2. The SI unit of mutual inductance is the henry, abbreviated H. (See Examples 30.1 and 30.2)
© 2005 Pearson Education
A changing current I in any circuit causes a self induced emf ε . The inductance (or self-inductance) L depends on the geometry of the circuit and the material surrounding it. The inductance of a coil of N turns is related to the average flux Φ B through each turn caused by the current I in the coil. An inductor is a circuit device, usually including a coil of wire, intended to have a substantial inductance. (See Examples 30.3 and 30.4)
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An inductor with inductance L carrying current I has energy U associated with the inductor’s magnetic field. The magnetic energy density u (energy per unit volume) is proportional to the square of the magnetic field magnitude.
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In an R-L circuit containing a resistor R, and inductor L, and a source of emf, the growth and decay of current are exponential. The time constant is the time required for the current to approach within a fraction 1/e of its final value. (See Examples 30.7 and 30.8)
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An L-C circuit, which contains inductance L and capacitance C, undergoes electrical oscillations with an angular frequency w that depends on L and C. Such a circuit is analogous to a mechanical harmonic oscillator, with inductance L analogous to mass m, the reciprocal of capacitance 1/C to force constant k, charge q to displacement x, and current I to velocity v x .(See Examples 30.9 and 30.10)
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An L-R-C series circuit, which contains inductance, resistance, and capacitance, undergoes damped oscillations for sufficiently small resistance. The frequency w’ of damped oscillations depends on the values of L, R, and C. As R increases, the damping increases; if R is grater than a certain value the behavior becomes overdamped and no longer oscillates. The cross-over between underdamping and overdamping occurs when R 2 = 4L/C; when this condition is satisfied, the oscillations are critically damped. (See Example 30.11)
© 2005 Pearson Education
END