Inductance.pdf

7/24/2019 Inductance.pdf

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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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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








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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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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








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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


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






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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






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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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Inductance.pdf