lecture chapter 36 v 1

8/12/2019 Lecture Chapter 36 v 1

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K7-27: RLC CIRCUIT -

COMPLETEK7-27: RLC

CIRCUIT - COMPLETE

K7-45: LOW AND HIGH PASS

FILTERS


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Chapter 36. AC Circuits

Today, a grid of AC

electrical distribution systems

spans the United States and

other countries. Any device

that plugs into an electricoutlet uses an AC circuit. In

this chapter, you will learn

some of the basic techniques

for analyzing AC circuits.Chapter Goal: To understand

and apply basic techniques of

AC circuit analysis.


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Topics: AC Sources and Phasors

Capacitor Circuits

RCFilter Circuits

Inductor Circuits

The SeriesRLCCircuit

Skip Section 36.6Power factor

Chapter 36. AC Circuits


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AC Sources and Phasors


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AC Sources and Phasors


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AC Circuits - Resistors

In an AC resistor

circuit, Ohms

law applies toboth the

instantaneous

andpeak

currents andvoltages.


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The resistor voltagevRis

given by

where VRis the peak or

maximum voltage. The

current through the resistor is

whereIR= VR/Ris the peak current.


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AC Circuits - Capacitors

The AC current to and from a

capacitor leads the capacitor

voltage by /2 rad, or 90.


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Capacitive Reactance

The capacitive reactanceXC

is defined as

The units of reactance, like those of resistance, are ohms.Reactance relates the peak voltage VCand currentIC:

NOTE: Reactance differs from resistance in that it does not

relate the instantaneous capacitor voltage and current

because they are out of phase. That is, vC iCXC.

V



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AC Circuits - Inductors

The AC current through an inductor lags the inductor

voltage by /2 rad, or 90.


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Inductive Reactance

The inductive reactanceXL

is defined as

Reactance relates the peak voltage VLand currentIL:

NOTE: Reactance differs from resistance in that it does not

relate the instantaneous inductor voltage and current

because they are out of phase. That is, vL iLXL.

AC Circuits - Inductors


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Inductive Reactance


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Homework set #4

Due Tuesday September 29thby 5PM

Same day as Exam INo late homework accepted

Exam I September 29th

Chapter 33-36 omitting section 36.6Make-up exams are oral; only valid excuses


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Last Time

E&M plane waves: Wave equation, B-fields relate to E-fields

Same amount of energy carried by E-field and B-field


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Last Time

Poynting vector and intensity:

Radiation pressure:

Polarization: Maluss Law:


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Last Time


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Last Time


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104 102 1 10-2 10-4 10-6 10-8 10-10 10-12wavelength (meters)

spectrum of visible light

106 108 1010 1012 1014 1016 1018 1020radio FM microwaves IR V UV x-ray gamma-ray

frequency (cycles/sec)

The Electromagnetic Spectrum

700 nmred

400 nm

violet

500 nm600 nm

7x10-7m 4x10-7m

5x1014

Hz 6x1014

Hz 7x1014

Hz4x1014

Hz


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Circularly polarized light:

I h t & C h t Li ht


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Incoherent & Coherent Light

http://skullsinthestars.com/2008/09/03/optics-basics-coherence/

I h t & C h t Li ht


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incoherent light(ordinary light sources,Hg arc lamp)

partially coherent light

coherent light(lasers, small pinhole)

Incoherent & Coherent Light

RC Fil Th (F i l i )


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RC Filters The concept (Fourier analysis)

Any waveform (like voltages driving your speaker when you play music) is a sum of

many sinusoidal waveforms of different amplitudes and frequencies.

The ac voltage generator depicted below for an RC circuit is idealized as ONE input

frequency, but in general could be a sum of MANY waveforms (like music) with

many frequencies.

Goal: Analyze the individual voltages across the resistor and capacitor when an input

waveform with any frequency wand voltage amplitude e0 is applied across both.

RC Fil A l i


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RC Filters Analysis

1. current is the same at all points in circuit at all time. Choose an

arbitrary current vector (time).

2. Phase: VRin phase with I, I in capacitor leads Vc

Amplitude: For a given I peak value, we know VRand Vc peak3. At any instant in time, we have (Kirchoffs loop law):

RC Filt A l i


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RC Filters Analysis

RC Filt A l i


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RC Filters Analysis


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RC Filt A l i


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RC Filters Analysis

Capacitor like a short at high frequencies since:

Voltage across Capacitor dominates at low frequencies

since:

If you input music, voltage across resistor would be like

treble and voltage across capacitor would be like bass. Build

your own speaker cross-over for woofer and tweeter.

LRC filt A l i


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LRC filters Analysis

LRC Filt A l i


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LRC Filters Analysis

1. current is the same at all points in circuit at all time. Choose an arbitrary current

vector (time).

2. Phase: Resistor VR in phase with I, I in capacitor leads Vc, I in inductor lags VL

Amplitude: For a given I peak value, we know VR, Vc and VL peak

3. At any instant in time, we have (Kirchoffs loop law):

LRC Filt A l i


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RC Filters Anal sis


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RC Filters Analysis



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lecture chapter 36 v 1

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