Class13HO

# Class13HO - Class 13 Impedance in AC Crcuits Physics 106...

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Class 13 Impedance in AC Crcuits Physics 106 Fall 2011 Press CTRL-L to view as a slide show.

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Learning Outcomes Last time we I learned about generators I looked at the details of a motional emf problem I reviewed for Exam #1
Learning Outcomes Today we will discuss: I Inductors and self-inductance I RL Circuit Problems I AC Circuit Terminology I R, L, and C in AC Circuits

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Inductors and Self-Inductance
Self-inductance I A coil of wire in a circuit is called an inductor. It produces a magnetic ﬁeld inside itself. I If the current is changing, it produces an EMF because its own B ﬁeld is changing in time.

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Self-inductance I If current is increasing, the inductor produces an induced current that opposes the current in the circuit.
Self-inductance I If current is decreasing, the inductor produces an induced current in the direction of the current in the circuit.

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Self-inductance I The faster the current changes, the larger the is the induced EMF
Self-inductance I We deﬁne the inductance L of a coil by the relationship: ± = - L Δ I Δ t I The negative sign indicates that a changing current induces an emf in opposition to that change

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Self-inductance I The SI unit of self-inductance is the Henry (H) I A useful expression for L is: L = - N Φ B I
RL Circuits

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Inductors in a Circuit I If an inductor, a resistor, a battery, and a switch are placed in in a series circuit: I Just after the switch is closed, the inductor produces an emf that completely stops the ﬂow of current - but only instantaneously I After a long time, the inductor acts like a wire.
RL Circuit I As the current gets larger, it changes less, and the inductor’s voltage decreases. I The time constant, τ , for an RL circuit is the time required for the current in the circuit to reach 63.2% of its ﬁnal value

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RL Circuit I The time constant depends on R and L τ = L R I The current at any time can be found by I = ± R ± 1 - e - t ²
Energy Stored in a Magnetic Field I An inductor stores energy in its magnetic ﬁeld. U L = 1 2 LI 2

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RL Circuit Example I A 3.0 Ω resistor, a 12 mH inductor, and a 12 V battery are connected in series. A switch is closed at t = 0.
AC Circuit Terminology

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AC Circuit I The output of an AC generator is sinusoidal and varies with time according to the following equation I V ( t ) = V max sin 2 π ft I V ( t ) is the instantaneous voltage I V max is the maximum voltage of the generator I f is the frequency at which the voltage changes, in Hz I The period is T = 1 / f
Average Voltage I V ( t ) = V max sin 2 π ft I The average value of sine is 0 I But that’s not useful

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Average Voltage I We could try V max | sin 2 π ft | I But absolute values are awkward functions.
Average Voltage I Try V 2 max sin 2 2 π ft I The average value of sin 2 is 1/2

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## This document was uploaded on 12/15/2011.

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Class13HO - Class 13 Impedance in AC Crcuits Physics 106...

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