§4: Real-Life DC Circuits - ECE User Home Pages

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Oct 7, 2013 (3 years and 8 months ago)

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x4:Real-Life DC Circuits
After a while of studying electrical engineering,you have seen only brief glimpses of how real devices work:this mini-chapter
provides a better-than-layman's understanding of how a couple di®erent household electronics work.Moreso than the rest of
the chapters,attention will be paid to understanding the basic concepts than absolute precision.In addition,many topics and
questions will combine many ¯elds of engineering,if nothing else but to show how electrical engineering works in unison with
other disciplines.
In each of the devices,we want to either process information in some form or perform a conversion of electrical energy into
other forms:mechanical,acoustical,etc.We will point out where such electrical transducers are used.Concepts will be used
from throughout the book,but will here be dominated by DC circuit analysis (Chapters 2-3).
Lightbulbs
Lightbulbs are perhaps the easiest form of modern electronic to analyze and model.They come in many shapes and sizes,so
we will assume a classical pear-shaped bulb.
Figure 1
Mechanically,lightbulbs consist of two rigid conductive poles with a Tungsten ¯lament between them,entirely encased in a
vacuum or inert gas.When electrical current passes through the Tungsten ¯lament,it gives o® light in an incoherent or random
fashion (for reference,the laser is a coherent light source),causing light dispersion all around.The chemically inert environment
is required so that the ¯lament does not catch ¯re (due to ambient Oxygen) and melt.
Lightbulbs are rated in terms of power,perhaps 60,75,or 100 Watts.This power rating can then be translated into a
corresponding ¯lament resistance (we will assume 120 Volt RMS value for the electrical outlet voltage).
100W lightbulb =)
(120V )
2
100 W
= 144­ resistor
Question:Why does it not matter that the input voltage to the lightbulb is AC rather than DC?Hint:consider the coherency
of the light emission.
The equivalent schematic for a 100 Wlightbulb is shown in Figure 4.2.
Figure 2
1
2
A more practical system than a single lightbulb would be the headlights and taillights of a car.Figure 4.3 shows a circuit with
many switches and bulbs:the switches are controlled by a combination of digital processors and mechanical switches (you\turn
the lights on"in most cars),while each bulb acts as a ¯xed resistance.
Figure 3
Another good example to consider is a string of Christmas lights.The cheaper set of lights contain bulbs strung in series,while
more expensive lights have the bulbs strung either in parallel,or in parallel segments.Figure 4.4 shows the circuit equivalents of
the two di®erent strings of lights.
Figure 4
Question:When a single bulb burns out in a string of Christmas lights,what is the result for the remainder of the circuit?
Answer:A burnt out bulb results in an open circuit;in the ¯rst string of lights,the open circuit of one bulb in series with
the others stops current conduction for the entire chain,and in the second string,the removal of a bulb has no e®ect on the other
bulbs.Why do you think the second set of lights is more expensive?
Hair Dryer
Hair dryers are among the simplest of all household heating devices:a device with the end goal of exchanging electrical power
delivered by a home wall outlet for controlled heating.The main parts of the hair dryer include a heating element able to convert
sinusoidal voltage into heat and a fan able to propel the heated air in a desired direction.
To begin the analysis,we model the heating element that converts this e®ective DC voltage to heat (we will again assume
an RMS equivalent wall voltage of 120 V),we only need to look at resistive heating elements.Chosen for both temperature
and voltage constraints,they convert the voltage well (and as always not quite perfectly)
1
to heat and have a roughly linear IV
relationship to be approximated by a resistor.A common physical heating element is a Nickel-Chromium(NiCr) wire coiled about
a ceramic core.
1
If you can visually tell the di®erence between a hot and a cold heating element then some of the energy output is in the optical spectrum.
3
Figure 5
The ceramic is electrically and chemically inert,but has wonderful temperature properties,and the wire is usually chosen to
have a resistance on the order of 10 to 20 ­.We may actually back-calculate from the power rating of an 800W hair dryer to
determine the equivalent resistance of the heating element (very little power is used up by the fan).
P =
V
2
DC
R
NiCr
=) R
NiCr
= 17:4 ­ for P = 800 W
Question:Given that the easiest way to vary the resistance of a NiCr wire,and thus the output power of the hair dryer,is
to change its length,specify how to switch from o®,low,medium,and high power settings.
Question:Repeat the question above if you are allowed two parallel heating coils.
The only remaining block is the fan:the electric current powers a small electric motor (perhaps a
1
4
W motor) which is
connected to a rotating set of fan blades.
Figure 6
Question:What is the noisy part of the hair dryer?(Do resistors produce sound?)
Question:Why does the fan speed change along with the power setting (consider thermodynamics!)?
The ¯nal schematic of our simpli¯ed hair dryer is shown in Figure 4.7.
4
Figure 7
The Telegraph
The ¯rst popular means of long-distance communication was the cable service:Samuel Morse's telegraph was the ¯rst device
in this communications revolution,and may be appropriately modeled as a base-3 digital electronic.Telegraph operators encode
information using one of three (hence the base-3 or tertiary description and moniker Morse code) signals:a blank pulse,a short
pulse,or a long pulse.These sequences can then be transmitted by closing the electrical contact of the telegraph machine,thereby
sending a current pulse down the transmission line.The operator at the other end of the line would then decode the\dit-dit-dah"
message and write out the communique.
Figure 8
As a circuit,the telegraph is trivial:a voltage source in series with a mechanical switch and a line resistance.The development
of AC transmission systems (telephone,radio,satelite) and better codes have greatly increased the bandwidth and feasibility of
long-distance communication.Modeling these AC circuits (in Chapter 7) will be the ¯rst step to understanding the more complex
systems.
Speakers
The speakers used in home and car audio systems give us our last example of a common simple DC circuit.The fundamental
goal of speaker is to convert electrical voltage or current into acoustical power or sound.Loosely,a speaker converts electrical
current °owing in a resistive wire into a magnetic ¯eld that controls the motion of a °exible cone.When the current in the coil is
negative,the cone is sucked inwards,while a positive current pushes the cone out.The IV relationship of the speaker is reasonably
linear,so we may model the speaker as a resistor;perhaps you have heard of 4­ and 8­ speakers.The basic mechanical structure
and rough electrical equivalent of the speaker is shown in Figure 4.9.
5
Figure 9
For a time-varying or AC current,the cone will change position at the same frequency that the current changes direction:
quickly varying signals (those of high frequencies) make the cone vibrate quickly,while slowly varying signals (those of low
frequencies) move the cone in slower,but often wider displacements.A common circuit is that of a two-channel car audio system
using four 8­ speakers.You should verify that the equivalent resistance of the of the four speakers is (8 +8)k(8 +8) = 8­.
Figure 10
To consider speakers in more depth,we need to develop additional mathematical tools to explain frequency selection in woofers
and tweeters,as well as power output and volume using apli¯ers.Once we have those tools,we will return to a more detailed
description of an audio system.