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hapter 30
Inductance
30-1 Mutual Inductance
30-2 Self-inductance and Inductors
30-3 Magnetic Field Energy
30-5 The L-C Circuit
30-6 The L-R-C Series Circuit
Physics 72 Bareza AY 15-16 1st sem 2
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Objective
Calculate mutually-induced EMF given the mutualinductance between two circuits
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Physics 72 Bareza AY 15-16 1st sem 4
Question:What if instead of straight wires we have coils?
Also, there is a changing current in one of the coils.
r
I
I
I and Iare both constant.
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Remember that:If the coils are in vacuum:
M21 is a constant. It depends on the geometry of both coils
(size, shape, number of turns, orientation
of each coil, separation between coils).
For our case, we assume that any magnetic
material present has constant Km so that M21 is
constant.
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For any two coils (symmetric or not):
SI Unit of mutual inductance M:
1 H = 1 Wb/A
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Equation to be used:
Example:
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Example:
Equations to be used:
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Seatwork:The figure shows two insulated coils wrapped around each
other with mutual inductance M = 0.5 H. If the current in coil 2
varies as I(t) = 8t2 + 2t + 14, what will be the induced emf in
coil 1 after 1 s?
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hapter 30
Inductance
30-1 Mutual Inductance
30-2 Self-inductance and Inductors
30-3 Magnetic Field Energy
30-5 The L-C Circuit
30-6 The L-R-C Series Circuit
Physics 72 Bareza AY 15-16 1st sem 11
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Objective
Calculate self-induced EMF given the self-inductance of thecircuit
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Any circuit that carries a varying current has an emf induced in it
by the variation in its own magnetic field.
It can occur in any circuit.
The effect is greatly enhanced if circuit includes a coil withN turns of wire.
Self-Induced emf
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Self-Inductance/Inductance
Since current i in the circuit changeswith time t,
From Faradays Law:
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Potential difference between the terminals of the inductor
If the rate of change of current is zero:
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Potential difference between the terminals of the inductor
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What is the physical significance of inductance L?
When L is large, the rate of change of current is small.
When L is small, the rate of change of current is large.
An inductor helps to prevent rapid changes in current.
So, what is the use of an inductor in a circuit?
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Example:
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Example:
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Physics 72 Bareza AY 15-16 1st sem 21
Seatwork:A current i flowing from a to b passes through an inductor of
inductance L, as shown in the figure. It is observed that the
potential at b is higher than at a.
Which of the following describes the current passing through
the inductor? increasing, decreasing or constant?
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hapter 30
Inductance
30-1 Mutual Inductance
30-2 Self-inductance and Inductors
30-3 Magnetic Field Energy
30-5 The L-C Circuit
30-6 The L-R-C Series Circuit
Physics 72 Bareza AY 15-16 1st sem 22
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Objective Calculate the total magnetic energy stored in an inductor
and its magnetic energy density after current is increasedfrom zero to a final-state value
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Energy Stored in an InductorThe total energy Usupplied while the current increases from
zero to a final value Iis
When the current decreases from Ito zero, the inductor
acts as a source that supplies a total amount of energy U.
When a steady current flows through an inductor,there is no energy flow in or out. .
Note:
This is actually storedin the magnetic fieldwithin the coil.
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Resistor vs. Inductor
A resistor is a device in which energy
is i r recoverablydissipated.
Energy stored in a current-carrying
inductor can be recovered when the
current decreases to zero.
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Magnetic Energy Density
Magnetic energy density in vacuum
Magnetic energy density in a material where = Kmo
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Example:
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Equation to be used:
Seatwork:How much current is required to store an energy of 7.2 kJ in
a coil with an inductance of 100 H?
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hapter 30
Inductance
OPTIONAL: *30-4 The R-L Circuit
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R-L CircuitA circuit that includes both a resistor and an inductor, and possibly asource of emf
Current growth
Current decay
1
2
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Current Growth in an R-L Circuit
Current in an R-L circuit with emf:
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Current Growth in an R-L Circuit
Time constant of an R-L circuit:
At time , the current has risen to or about
63% of its final value /R.
Current in an R-L circuit with emf:
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What is the current through the ideal battery after a very
long time the switch S is closed?
Example:
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Current Decay in an R-L Circuit
Current in an R-L circuit:
Io: initial current in the circuit
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At time , the current has decreased to or
about 37% of its initial value Io
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Current Decay in an R-L Circuit
Current in an R-L circuit:
Io: initial current in the circuit
Time constant of an R-L circuit:
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Example:
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Seatwork:For the circuit shown, find the currents I1, I2, and I3(a) immediately after switch S is closed and
(b) a long time after switch S has been closed.
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hapter 30
Inductance
30-1 Mutual Inductance30-2 Self-inductance and Inductors
30-3 Magnetic Field Energy
30-5 The L-C Circuit
30-6 The L-R-C Series Circuit
Physics 72 Bareza AY 15-16 1st sem 38
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Objective
Describe the charge and current variation in time in an L-Ccircuit
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L-C CircuitA circuit that includes both an inductor and a capacitor
Both charge and current in an L-C circuit oscillate sinusoidally with time, with an
angular frequency of
Capacitor charge:
Current in the circuit:
If at time t= 0:
the left-hand capacitor plate hasits maximum charge Q and the
current i is zero, then
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L-C Circuit
Capacitor charge:
Current in the circuit:
Q
Imax
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Energy in an L-C Circuit
Capacitor charge: Current in the circuit:
Imax
= Q
Total energy of the LC circuit:
Recall:
The total energy
in an LC circuit isconstant.(inductor) (capacitor)
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Example:
Use the following equations:
(a) Since = , = 1 then = (b) = 1 (c) Energy =
1
where = ()
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Seatwork (4 pts):
Use the following equations:
(a) = 4(b) =
(c) = 1
(d) = 2/
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hapter 30
Inductance
30-1 Mutual Inductance30-2 Self-inductance and Inductors
30-3 Magnetic Field Energy
30-5 The L-C Circuit
30-6 The L-R-C Series Circuit
Physics 72 Bareza AY 15-16 1st sem 45
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Objective Describe the charge, voltage and current variation in timefor underdamped, critically damped and overdamped L-R-C
circuits
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L-R-C Series CircuitAn inductorwith inductance L and a resistorof resistance Rare
connected in series across the terminals of a chargedcapacitor.
1.Underdamped oscillation
2.Critically damped
3.Overdamped
3 cases:
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Underdamped CRITICALLY damped OVERdamped(Small R) (Large R) (Very large R)
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Example:An L-R-C series circuit includes a 2.0- resistor. At t = 0 the
capacitor charge is 2.0 C. For which of the following
values of inductance and capacitance will the charge on the
capacitornot oscillate?
A. L = 3.0 H, C = 6.0 F
B. L = 6.0 H, C = 3.0 F
C. L = 3.0 H, C = 3.0 F
Hint:
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Seatwork (1 pt):Consider an R-L-C series circuit with resistance 1 . Which
values of inductance L and capacitance C will the charge on
the capacitor undergo a damped oscillation?
A. L = 1.0 H, C = 4.0 F
B. L = 3.0 H, C = 12.0 F
C. L = 3.0 H, C = 18.0 F
D. L = 3.0 H, C = 6.0 FE. L = 1.0 H, C = 8.0 F
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