Physics 11b Lab 2: Current, Ohm’s Law, Resistance, EMF

1. Relationships between Voltage and Current

Goals: Determine the current to voltage relationships for a 150 Ohm resistor, an

LED, and light bulb. Understand the basic mechanisms that govern IV

relationships, and consider symmetry and hysteresis as they apply to light

emitting devices. Study the power consumption of the devices. Measure the

relative energy efficiency of the LED and the light bulb.

a.! Materials: 150 Ohm resistor; 100 Ohm Resistor ; 1 BNC T ;1 BNC to

banana;4 BNC cables;4 micrograbber to BNC; function generator; multimeter

Measure the IV (current to voltage) curve for a 150 Ohm resistor using the

function generator as a voltage source for a voltage range of +-5V. You could use

a source with a voltage that is constant as a function of time, but this is very

tedious. You can use the signal generator to produce a voltage that changes

slowly with time. If the change is slow enough, the circuit will be in equilibrium,

so you can apply the results from Chapter 4 to the IV relationships. Thus, you

can measure the IV curve by changing V with time and measuring the resulting

current as a function of time.

Apparatus Assembly Directions 1. Setup the scope to monitor the signal generator

a.! Connect the BNC T shown on the left in the figure above to the output of the

signal generator that is highlighted by the light blue arrow in the image on the

right above.

b.! Make sure that none of the buttons highlighted by the purple rectangles

depressed. If any are, press on the button and it should pop out.

2. Setup the signal generator to produce a 5 V amplitude triangle wave at 20 Hz

a.! Turn on the signal generator on by pressing the button highlighted by the

purple arrow.

b.! Connect the output of the signal generator to CH1 on the scope using a BNC

cable connected to one side of the BNC T on the output of the signal generator.

c.! Choose the triangle wave output by depressing the button indicated by the

pink arrow.

d.! Use the signal on the scope to adjust the signal generator to produce a triangle

wave with a 5 Volt amplitude and a 20 Hz frequency. The amplitude is

controlled by the knob highlighted by the yellow circle. Get the 20 Hz

frequency by pressing the 100 Hz frequency choice button ( indicated by the

dark green arrow) and tuning the coarse frequency adjustment

knob(highlighted by the red circle) until the frequency display reads 20 Hz. If

the displayed frequency changes by more than 1 Hz after you have let go of

the knob for more than 10 seconds, then ask for assistance.

3. Connect the circuit

a.! Place the 150 Ohm resistor in the breadboard

b.! Connect the Logger Pro current sensor in series with the resistor, as shown in

the schematic and image above

c.! Connect a second BNC cable to the BNC T on the output of the signal

generator

d.! Connect a jack/micrograbber combination to the end of this BNC cable, and

then use the micrograbbers to connect the voltage source in parallel with the

series combination of the resistor and the current sensor, as shown in the

schematic and image above.

e.! Connect a Logger Pro voltage sensor in parallel with the resistor. Use the

voltage probe with the wires permanently attached to the alligator clips. Place

each of the wires in the voltage sensor alligator clips into a hole in the same

column as each of the two resistor lead wires as shown in the image above.

4. Setup Logger Pro to acquire data

a.! Make sure the spectrometer is NOT connected to the USB port on the

computer. If it is connected, it will make data acquisition extremely slow.

b.! Make sure that the LabPro Box is connected to the USB input on the computer.

c.! Connect the LoggerPro probes to the LabProb Box.

i.! Connect the LoggerPro voltage probe with the alligator clips that are

permanently clamped around wires to the input of channel 3 on the

LabPro Box.

ii.! Connect the voltage probe with the unmodified alligator clips to the

input of channel 1 on the LabPro Box.

iii.! Connect the current sensor to the input of channel 2 on the LabPro

Box.

d. Start IV Template.cmbl. This is a LoggerPro program that will assist you in

taking data. This program should be on the desk top, but if it is not you can

download it from the 15b website. A screen shot of the program is shown

below with annotations added to explain the meaning of each plot.

Meaning of the program display

e.! The upper left box shows the voltages as a function of time. For section 1a

you are using only 1 voltage probe, and its output should be on channel 3. The

output channel 3 is plotted in green, and the output of channel 1 is plotted in

red. The voltage for channel 1 should always be zero for section1a.

f.! The lower left box shows the current as a function of time. This should

appear in column 2.

g.! The box on the right shows a plot of the current flowing through the resistor,

IR, as a function of the voltage across the resistor, VR.

5. Tune the signal generator to the setting for data acquisition and begin data

acquisition

a.! Set the signal generator to 0.2 Hz by depressing the 1 Hz frequency button

highlighted by the bright green arrow. Do not change the frequency

adjustment knobs. The frequency display sometimes shows odd values at

these low frequencies, but the signal generator output should be at 0.2 Hz.

b.! Start data acquisition.

c.! Measure the IV curve for a 0.20 Hz triangle wave. The data should resemble

the window on the upper right.

i.! manually.

d.! Troubleshooting: Skip this if everything is working.

i.! If the scaling on the graphs is bad

1.! You may want to rescale some of the curves so that they

occupy most of the space in the graph, making them easier to

read. Try autoscaling first. To get autoscale right click on the

window and choose autoscale. If LoggerPro makes bad

choices using autoscale, rescale the plot

ii.! If the current is not appearing on CH2 or the voltage across the

resistor is not appearing on Ch3, then do the following.

1.! Quit LoggerPro

2.! Correct the connections to the LabPro Box so the current is on

CH2 and the voltage across the resistor is on channel 3. The

other voltage probe should be connected to CH1. Restart IV

Template.cmbl. If the data acquistion still not working, please

ask for immediate assistance.

Is it ohmic? Calculate the effective resistance as a function of voltage. Hint:

If you click on the IV curve, then choose “Analyze” from the toolbar, a

dropdown menu will appear. Choose linear fit, and a LoggerPro will calculate

the slope and intercept of the line and print the values in the window. How

does the measured resistance compare with the nominal resistance? Is the

device symmetric? Is it hysteretic? Note: you would get the same results for

a 20 Hz triangle wave.

Bonus: Repeat with a 20 Hz triangle wave.

2. What comes out of the wall?

Goal: Learn about the form in which electrical power is delivered to consumers

in the US.

a.! Materials: light source box; scope probe; scope; multimeter; wet paper towel

Electricity is delivered in the form of an alternating current (AC) signal where

the voltage and current vary sinusoidally with time. Different countries have

different standards. AC voltmeters read the RMS values of the current and

voltage. Ask someone on the laboratory staff to use an AC Voltmeter to

measure the voltage difference between the hot, ground, and neutral outputs of

a standard duplex wall plug, such as the one shown below. A detailed

discussion of power generation and delivery in the US is given in a

supplemental information section. What is the measured voltage difference

between hot and ground? What is the measured voltage difference between

hot and neutral? What is the measured voltage difference between neutral and

ground?

Bonus: Measure the resistance across your body by holding the Ohmeter

leads in your hands. Compare to the resistance across one hand. Compare

with the resistance across your body when your hands are wet. Compare with

the resistance when your hands are wet with salt water. How much current

would flow through those three resistive paths if a 110V AC potential was

connected to those points on your body. How does this compare with 5 mA,

the “safe current?”

b. Materials: Scope; light box, BNC cables, scope probe

The two images above illustrate the connections to the lightbox. For this

section of the lab, you will just use the lightbox to monitor the AC voltage

coming out of a wall socket. The lightbox just makes this experiment safer.

Apparatus Assembly Directions 1. Setup the scope to monitor the AC voltage coming from the wall using the light

box

a.! Monitor the voltage difference between hot and ground on Ch1

i.! Attach the scope probe to the light box as shown in the image on the

right above

1.! Attach the scope probe micrograbber to the wire loop inside

the box behind the slot. The slot in the lightbox has a wire

loop to which the micrograbber on the scope probe can be

attached.

a.! The wire behind the slot is connected to the hot output

of the wall socket; therefore, the central pin of the

BNC for the scope probe is attached to the hot voltage

coming from the wall.

2.! Attach the alligator clip on the scope probe to the ground

terminal on the outside of the lightbox.

a.! The outside of the BNC is not connected to the ground

coming from the wall.

ii.! Connect the BNC output of the scope probe to the input of CH1 on

the scope.

b.! Monitor the voltage difference between neutral and ground on Ch2

i.! Connect the BNC jack on the light box that is labeled neutral to

channel 2.

a.! This jack is connected so its center pin is at the neutral

potential, and the outside of the BNC is at ground.

c.! Adjust the scope settings so that several cycles of the 60 Hz frequency are

visible on the scope.

2. Finish setting up the light box a and begin data acquisition

a.! Plug the cord on the light box directly into the wall socket

b.! Adjust the voltage scale on the scope so that you can clearly read the signals

on CH1 and Ch2.

Channel 1 shows the difference between hot and ground. How well is CH1

described by V = 170 Sin (2 ! 60 t)? How do the measured peak to peak values

compare with voltage reading on the AC voltmeter when it was connected between

hot and ground? Channel 2 shows the voltage difference between neutral and ground.

Is it zero? How can there be a voltage difference between neutral and ground if the

two are connected at the breaker box?

3. Efficiency of the conversion of Electrical Power to Light

Goal: Understand the basic mechanisms that transfer electrical energy to optical

energy in light sources. Compare the energy efficiency of different electrically

powered light sources. Study the properties of the light emitted by the different

sources.

Divide the class so that at least one group does each of the light sources: 1.

incandescent light bulb; 2. compact fluorescent light bulb; 3. LED spotlight. Each

group will do the same experiments, but with the different bulbs

a.! Materials: light emitter and lightbox;variac; photodiode; spectrometer;

temperature sensor; ruler; scope;scope probe;BNC cables, Labview

A schematic of the light box and its connections to the scope are shown in

the schematic diagram in the left hand section of the image above. The

other two images in the figure show photographs of the wiring inside the

box. In the central image, each of the wires is highlighted and labeled,

where red is hot, white is neutral, green is ground, and yellow is V3. In the

right hand image, the wires are visible. Wires at the hot voltage are shown

in red and wires at the neutral voltage are shown in gray.

Apparatus Assembly Directions

1. Setup the scope to monitor voltage across and current flowing through a light

emitter, as well as the intensity emitted.

a.! CH1 already displays the potential difference between hot and ground as

monitored by the scope probe. This connection is still correct, so no change

is required.

b. CH2 already displays the potential difference between neutral and ground.

This connection is still correct, so no change is required.

c. CH3 will monitor the voltage across the 1 Ohm resistor that is connected in

series with the light emitter.

i. Connect the BNC jack labeled 1 Ohm to the input of CH3 on the

scope using a BNC cable. How is this voltage related to the

current flowing through the light emitter?

d.! CH4 will monitor emitted light by the device, which is proportional to

measuring the voltage generated across the leads of the photodiode.

i.! Connect a micrograbber to BNC to the leads of the photodiode

ii.! Connect the jack on the micrograbber to BNC connector to a BNC

cable that is in turn attached to the input of channel 4, so CH4

displays the emitted intensity as a function of time.

iii.! Hang the photodiode so that it can measure the light emitted by the

light source without your having to hold it. It is convenient to hang

the photodiode from a chemistry stand where the diode is

approximately 1 cm from the light source. Be careful to avoid

saturating the photodiode.

e.! Make sure all 4 channels are displayed on the scope.

2. Setup the variac to control the voltage difference between hot and neutral.

a.! Connect the plug from the lightbox to the outlet on a variac, and connect the

variac to a wall plug. An image of a variac is shown above. The wheel on

the top of the variac controls the RMS amplitude of the AC voltage coming

out of the variac. You will use the variac to control the RMS voltage

suppled to your light box, which in turn controls the voltage across the light

emitter.

b.! Set the knob so that the line points to 0 volts

c.! Turn on the variac by flipping the power switch.

3.! Begin data acquisition

a.! Start the Labview program entitled 15b_lighting.vi. It will not acquire data

if all 4 channels are not displayed on the scope. A screen shot is shown

below.

Meaning of the items in the program display.

i.! The green curve on the left shows the RMS current IRMS flowing through the light

emitter as function of VRMS, the voltage across the light emitter. IRMS= (CH3-

CH2/1 Ohm) and VRMS is CH1-CH3.

ii.! The lavender curve on the right shows the emitted intensity vs the RMS power.

b.! Begin slowly and smoothly turning the knob on the variac and continue

turning until the knob points to 120 V. DO NOT TURN THE VOLTAGE

ABOVE 120V!!! As you turn the knob, you change the voltage supplied to

the lightbox. The plots on the program should changes as you turn the knob.

When you reach 120 V, the program should display an IV curve for voltages

from 0 to 120 V. It should also display intensity as a function of electrical

power for voltages from 0 to 120 V. Turn the voltage slowly and smoothly

back down to 0 V and click on the stop button on the program.

Does your device emit light for all input voltages? If not, at what voltage does the

device turn on? For voltages where the device emits light, does the intensity increase

significantly with voltage? For voltages where the device emits light, does the ratio

emitted intensity to electrical power increase or decrease with increasing power. Sketch

the relative efficiency of the conversion of electrical power to optical power as a

function of applied voltage. Is it linear? Explain your result

Apparatus Assembly Directions

1. Setup the spectrometer to measure the intensity as a function of frequency for

the light emitted by the light sources as a function of the voltage across the light

emitter.

a.! Disconnect LabPro from the USB connection on the computer. If it remains

connected, the spectrometer will not work.

b.! Place the spectrometer so the hole is facing the light source.

2.! Finish the setup the spectrometer to and begin data acquisition

a.! Start the program called light spectrum that should be on the desktop. This

program operates the spectrometer for you and displays the resulting data, as

shown in the screen shot below.

Meaning of the program display

a. The line shows the intensity as a function of wavelength. The rainbow in the

back shows the color that corresponds to each wavelength.

b. Several different spectra can be obtained

The equation above gives the relationship between the temperature of an object and its

emission spectrum. The pink curves in the image below the screen shot show the

intensity as a function of wavelength for four different temperatures, where again the

rainbow shows the color corresponding to that wavelength. As you can see, cooler

objects emit light that is redder and less intense than hotter objects. You can use the

graphs to estimate temperatures of the light emitters studied in this section.

For comparison, the emission spectrum for the sun is shown in the figures on the

left. The top left figure shows the distribution for a temperature approximately equal to

the temperature at the surface of the sun. The wavelength scale is much larger, so the

rainbow only occupies a small fraction of the figure. The bottom figure has the same

wavelength scale and shows the measured intensity as a function of wavelength for

sunlight, where the black curve shows the predicted curve for an object with a

temperature of 5250 C. Notice only about 1/3 of the light emitted by the sun falls within

the visible wavelengths.

Data Taking Steps

1. Turn the Variac to 40 V. Leave the voltage constant.

2. If the light emitter is emitting light, take a spectrum at 40 V. Otherwise skip to step 4.

3. Click on the stop button when you are satisfied with the spectrum.

4. Turn the variac up to 60 V. Leave the voltage constant.

5. If the light emitter is emitting light, take a spectrum at 60 V. Otherwise skip to step 7.

6. Hit the collect button again and choose the option to keep collecting in the same

graph.

7. Click on the stop button when you are satisfied with the spectrum. Both spectra

should be displayed at the same time.

8. Turn the variac up to 110 V. Leave the voltage constant.

9. Hit the collect button again and choose the option to keep collecting in the same

graph.

10. Click on the stop button when you are satisfied with the spectrum. All 3 spectra

should be displayed at the same time.

Does the spectrum of your source change with voltage? How does your

measured spectrum the solar spectrum shown above? Is the emitted spectrum

well described by a black body at some temperature T? If so, what

temperature? If not, what is the origin of the light and what determines its

color? Are there any narrow features in the emission spectrum? If so, what is

their origin.

Bonus: Use the curve fit option to fit the spectrum to a Gaussian.

Bonus: For the maximum voltage, measure the photo-detector current as a

function of distance from the bulb. Note Solid state temperature sensors

exploit the temperature dependence of conductivity.

Bonus: 1. measure the angular dependence; 2. calculate the actual total power

conversion from electrical power to optical power. Hint: the conversion

efficiency of a photodiode is approximately 50 microamps per mW/cm2.

b.! Present and explain the results.

Supplemental Information

Breadboards

Breadboards are used to quickly create model circuits without creating the mass of wires

that would be required to connect everything with alligator clips or micrograbbers. An

image of a breadboard is shown on the left below. They consist of a series of holes into

which the leads from circuit elements can be inserted. Leads are the wires that stick out

of circuit elements and allow them to be connected. The holes are connected on the back

of the breadboard as shown in the diagram on the right below, where the light blue lines

indicate holes that are electrically connected. The holes between the red and blue ones at

the top and the bottom of the breadboard are connected horizontally. They are usually

used to distribute the voltage from the power supply to the circuit. The two central

regions are electrically connected in columns. They are used to connect circuit elements

to each other. The photograph in the center below shows the back of the breadboard with

part of the protective insulation peeled off. The metal strips that connect the central

columns and the edge rows are clearly visible.

An image of a circuit and the equivalent schematic are shown below as an example.

Spectrometer Use Instructions

Use a USB cable to connect the Vernier Spectrometer to the computer. (Note: Do

not connect the spectrometer to a USB hub.) The Spectrometer is powered by your

computer through the USB cable.

2. Start the Logger Pro 3.4.5 software.

3. Select Connect Interface !!Spectrometer !!Scan for Spectrometers from the

Experiment menu.

4. To calibrate the Spectrometer, choose Calibrate !!Spectrometer from the

Experiment menu. The calibration dialog box will display the message: “Waiting

…seconds for lamp to warm up.” (see Figure 1) The minimum warm up time is

one minute. NOTE: For best results, allow the spectrometer to warm up for

at least three minutes. Follow the instructions in the dialog box to complete the

calibration. Click OK.

Figure

5. Choose Change Units !!Spectrometer !!Intensity from the Experiment menu.

Intensity is a relative measure.

6. Aim hole in the spectrometer at the light source. Click . Observe the

graph of intensity vs. wavelength. Click to end data collection. Note: If

the spectrum maxes out with flat tops to peaks, reduce the integration time.

The screen will then display intensity as a function of wavelength, where the graph is

overlayed on a rainbow that displays the color corresponding to that wavelength.

Symmetries in Physics In the discussion above, we compared the IV curves for a positive voltage across a device

and compared that to the result for a negative voltage. If the device is uniform, then the

ratio of I to V for the two systems should be identical. If the device has different

properties at one end than at the other, then the two results may not be identical. This

system is essentially one dimensional; therefore, if the device is invariant under

translation along the current carrying direction (shown in the figure below as the device

having the same purple property everywhere), it is also invariant under reflection about

its center. In this case, the result of all four physical measurements shown must be

exactly the same. In contrast, if the device has two different sides with different

properties, then it is not invariant under translation or reflection. Such a device is shown

below with red and blue sides where the two sides have physically distinct properties.

Measurements where one sets up two sets of experiments that should be identical if a

symmetry exists, but may yield different results if the symmetry does not exist have and

continue to play a vital role in our understanding of the basic properties of the universe.

http://www-project.slac.stanford.edu/e158/parityviolation.html

http://ccreweb.org/documents/parity/parity.html

Symmetry is one of the most important concepts in physics. Emily Noether

showed that conservation laws in physics are linked symmetries in the mathematical

formulation. Conservation of energy, momentum, and angular momentum are

associated with invariance as a function of translation in time, position, and angle

respectively. There are many other more subtle symmetries in physics. Until 1957,

inversion, or mirror, symmetry was expected of nature. It came as some surprise that

parity, P, symmetry is broken by the radioactive decay beta decay: electrons from the

beta decay are preferentially emitted in the direction opposite that of the aligned

angular momentum of the nucleus process a discovery made by C.S. Wu and her

collaborators. When it is possible to distinguish these two cases in a mirror, parity is

not conserved. As a result, the world we live in is distinguishable from its mirror

image. At present there is no proof that the combination of CPT (charge,parity, and

time) is not conserved, that is the universe looks the same if CPT are ALL reversed.

Evidence for CPT symmetry violations are eagerly sought

http://www.physics.indiana.edu/~kostelec/faq.html

http://www.atomic.princeton.edu/romalis/CPT

Great care must be taken to determine that observed changes are due to variables

controlled by the experimentalist. Sometimes experimental conditions that are assumed to

be identical are not because some important variable has been ignored. For example,

Jerry Gabrielse research group at Harvard suddenly got different results when the subway

connection from Harvard Square to Alewife opened. They were still doing exactly the

same experiments, but the magnetic fields associated with the running of the subway

changed the conditions in their lab. Sometimes, the phase of the moon even matters.

http://news-service.stanford.edu/news/2000/march29/linac-329.html

http://accelconf.web.cern.ch/accelconf/e00/PAPERS/MOP5A04.pdf

http://www.agu.org/pubs/crossref/2003.../2001JB000569.shtml A crucial aspect of

experimental physics is sorting out what factors determine the outcome of your

experiment.

Resistor Color Code

Additional Capacitor Information In this lab you are using ceramic capacitors. You used electrolytic capacitors in the

previous lab. Ceramic capacitors typically have smaller capacitance, but are more ideal

than electrolytic capacitors: electrolytic capacitors leak more and show inductive

behavior at high frequencies. Also, unlike electrolytic capacitors, ceramic capacitors are

not polar. Voltage and capacitance ranges for different types of capacitors are shown

below, and additional discussion of capacitor types and applications is available.

http://www.electrosuisse.ch/display.cfm?id=113982

Diodes

In a vacuum diode, the motion of the charges is particularly simple since there are no

collisions, as discussed in section 4.2. Vacuum diodes are still used in some specialty

applications such as ion gauges where the very rare collisions between ions allow low

pressures to be measured ; however, in most cases they have been replaced by semi-

conductor diodes consisting of a P doped semi-conductor (positive free carriers) adjacent

to an N doped semiconductor (negative free charge carriers). An excellent applet shows

the current to voltage relationship for a diode . Semiconductors are discussed in section

4.9 of Purcell.

Photodiodes

Photodiodes produces a current that is proportional to the light intensity hitting the diode,

so when a voltmeter is connected to its leads, the current will flow through the resistor in

the voltmeter resulting in a voltage difference that appears at the voltmeter output. A

photodiode is basically an LED operating in reverse: the internal electric field of a PN

junction is used to separate an electron hole pair created by a photon hitting the diode.

The same principle is used in solar cells to generate electricity from sunlight

US Electrical Power Distribution System

The power generated by power stations has voltage that changes periodically as a

function of time. In the United States at a wall outlet, the voltage as a function of time is

approximately V = 170 Sin (2 ! 60 t) a sine wave with a frequency of 60 cycles/second

with a root mean square(RMS) voltage of 120 V, corresponding to an amplitude of 170 V

and a peak to peak excursion of 340 V. The root means square value of an AC voltage is

equal to the amplitude of the voltage divided by the square root of 2. AC has at least

three advantages over DC in a power distribution grid:

1.! Large electrical generators generate AC naturally, so conversion to DC would

involve an extra step.

2.! Transformers can either increase or decrease the voltage. In power supply

systems a chain of transformers changes the voltage in steps from 155,000 to

765,000 V at the power plant to 110 V at the wall plug. Transformers must have

alternating current to operate

3.! It is easy to convert AC to DC but expensive to convert DC to AC, so if you were

going to pick one or the other AC would be the better choice.

Electrical Power Delivery in the US

All power companies use an alternating current transmission scheme with long range

transmission voltages sometimes in excess of 100,000 volts, with long distance transmission at

voltages from 155,000 to 765,000. The Three wires leave the power station, where there is a

phase delay of 120 degrees between each of the three wires, as shown below.

V1=Vo sin[ 2!"#$t] V2=Vo sin[ 2!"#$t -2 !/3] V3=Vo sin[ 2!"#$t -4 !/3]

Three phase systems are frequently used in to power large electric motors, but most residences

get only 1 phase power.

Local Distribution Power is brought down from the high voltage transmission towers to substation transformers.

Substation transformers lower the voltage for local distribution via power poles. The power pole

line can come all the way to your home or be converted to an underground distribution system for

the final leg to your house. Only one phase is required for residential applications, so at some

point there is a tap that attaches to only one of the three phases. Another transformer steps the

one phase voltage down to the two 120 volt circuits, plus a neutral wire, to your house. A photo

of a typical pole transformer that converts 7200V to 120V is shown below, with an electrical

schematic of the transformer shown at right. Some systems now use14,400 V instead of 7200.

Transformers are treated in Purcell in Chapter 7. New federal regulations require that the energy

efficiency of pole transformers increase by 2010. One increased efficiency is provided by

changing from changing the internal wiring form Aluminum to Copper because copper has a

higher conductivity.

The one phase voltage is shown at the top of the pole, with the ground wire even with the

top of the transformer. The 7200 V is the difference between the one phase voltage and

the ground. This is fed into one side of a transformer. The other side is a center tap

transformer with three outputs. The three output wires leave the transformer and enter

your house, as shown in the diagram on the right above. The voltages as a function of

time are shown below for a total time interval of 0.1 seconds. The blue corresponds to

the far left wire, the green corresponds to the central wire, and the red corresponds to the

far right wire. The red and the blue are 180 degrees out of phase, so the three voltages are

Vblue =170 sin[ 2!"60t] , Vgreen =0 , V red=170 sin[ 2!"60t+!]

Notice that the green is the sum the red and the blue. Most residential power applications

use a connection between one of the hot wires (either red or blue) and the green wire. This gives

110 V RMS 60 cycle power. Some appliances, such as electric dryers use 240 V RMS. This is

obtained by using the difference between the hot wires, shown by the purple line below, where

the other lines are the same as those shown above.

.

Power Meter The power meter measures the power entering your house. A photo of a typical power meter is

shown above. The power meter is in line with the power feed from your nearest transformer. The

Watt is the unit of electrical energy. One kiloWatt-hour is equivalent to the use of 1000 Watts of

electricity (ten 100-Wattbulbs) for one hour. A kiloWatt-hour varies with location. Hawii is the

most expensive at 21.48 cents/kW-hour. Massachusetts is third most expensive at 15.13 cents.

Idaho is cheapest at 4.91 cents. The US average is 8.77 cents.

http://www.eia.doe.gov/fuelelectric.html A nice map of price by state is given at

http://www.eia.doe.gov/fuelelectric.html

Load Centers A load center is positioned between a breaker box and the power meter. They are located near the

power meter and therefore are frequently found in your garage. The load center has one big

breaker for each of the 120 volt circuits from the power meter. A typical main breaker in a load

center is 150 amperes (amps)

Breaker Boxes The diagram below shows the pole transformer picture above producing the two 120 V AC

signals plus the neutral voltage, where the red, light green, and blue correspond to the colors in

the voltage plots above. The dark green shows the connection to the ground. The neutral and the

ground are attached at the breaker box, so they represent the same voltage.

The red and blue power feeds are connected to two power buses located behind the circuit

breakers. The upper breaker highlighted in blue corresponds to a 110V circuit. The black wire

that comes down from the breaker corresponds to the black wire shown at the bottom in the three

wire set that goes out to the wall outlet. The white wire going to the wall outlet is attached to the

neutral, and the beige wire is attached to the ground. The lower left hand breakers in the diagram

above (pink 30-amp ganged breakers) correspond to the 240 V circuit that goes out to the dryer in

the picture above. The top breaker in this pair, with the black wire leading to it, is connected to

one 120 volt bus attached to the blue wire shown coming into the top of the box from the pole

transformer. The bottom breaker in this pair, with the red wire leading to it, is connected to the

other 120 volt bus that is attached to the red wire coming from the pole transformer into the box.

The white wire is connected to the neutral, and beige wire is connected to the ground. The

difference of voltages on the red and black wires is 220V rms. The difference between the black

and the white is 110V RMS, as is the difference between the red and the white.

House Wiring

Now let's take a look at the wall outlet circuit that starts with the black wire leading down from

the top left 20-amp breaker in the breaker box image above. This is a single 120 volt circuit that

will service 2 or 3 wall outlets. If we follow this wall outlet circuit out to a duplex wall outlet, it

will be wired as follows:

http:// www.cornerhardware.com/howto/images/ht052_1.jpg

Note that the vertical slot to the left is longer than the one to the right, to distinguish the hot wire

from the neutral wire. If the outlet is wired properly, the white wire is connected to the longer

neutral slot to the left and the hot black wire is connected to the short slot to the right. The

semicircular connection below the slots is connected directly to the ground outside the house. It

is not connected to the neutral except at the breaker box. The wiring for a 220V four plug

receptacle is shown at right. Again, the semicircular slot corresponds to ground. In this case,

BOTH of the side slots are hot and connected to the two out of phase 110V bus bars, so the

difference between them is 220V. The lower L shaped connector is the neutral. The outer case of

an appliance should always connected to the safety ground, so it doesn't make much difference

what happens to the other wires. If the neutral wire shorts to the case nothing happens. If a hot

wire shorts to the case, a short circuit is presented to the breaker and it should open. The safety

ground prevents YOU from being the path for a circuit from a hot wire shorted to the case to

ground.

Much of the information and many of the pictures in this document were adapted from http://www.the-appliance-clinic.com/electwiring.html and

http://science.howstuffworks.com/power.htm/printable

Electricity Generation and Distribution to the Local Network

The physics underlying electrical power generation is covered in Chapter 7 of Purcell, but the

material below gives an overview of the energy sources that are used to produce electrical power,

and the physical infrastructure used to transfer the power from the power stations to users. The

discussion above began with the long distance transmission lines, but there are two earlier stages :

the generation of the power at the power plant and the increase in voltage that occurs before the

long distance transfer begins. All the steps are shown below in a diagram from How Stuff Works,

where I have added the voltage levels that are typical at each stage. The second image below is

from Encarta. It shows the actual values of different long haul distribution lines, as well as

showing the few High Voltage Direct Current lines that now exist. High voltage direct current

is becoming more attractive for reasons including: improved electronics allow better

conversion between AC and DC; the feasibility of linking AC power grids whose phases

are not synchronized; reduced losses in comparison to AC in very long haul applications

where the capacitance of the wires becomes important; http://en.wikipedia.org/wiki/High-

voltage_direct_current

It may at first seem odd that such high voltages are used for power transmission, and that there is

an effort to keep increasing the voltages not only for long distance transmission, but also for

transmission from power substations to pole transformers. The answer is that increasing the

voltage reduces the energy lost as the power is transmitted. Transmitting electricity at high

voltage reduces the fraction of energy lost to heating. Consider an electrical power

delivery system that must deliver a power P=IV where I is the current and V is the

voltage. Let a metal power line be characterized by a resistance R. (In chapter 8 of

Purcell complex reactance will be introduced, allowing one to include AC signal losses

due to the capacitance of the cable, but the basic scaling laws of power efficiency vs

voltage are the same). The energy lost in the transmission line is then I2R=(P/V)

2 R.

Thus the power loss decreases inversely with the square of the voltage and proportional

to the resistance, driving one to try to increase energy efficiency by increasing line

voltage. This process cannot go on without limit, At voltages larger than 2,000 kV

corona discharge losses are so large that they can offset the lower resistance loss in the

line conductors. A nice video of a corona discharge is available. Transmission and

distribution losses in the USA were estimated at 7.2% in 1995 , and in the UK at 7.4% in

1998.

As discussed above, low electrical resistance in cables can also improve energy

efficiency; however, the installation and maintenance costs have favored higher

conductivity materials. Thus aluminum is often used in transmission lines, though its

conductivity is small than copper because its cost is lower as is its conductivity to weight

ratio The issue of long term energy efficiency due to improved conductivity vs short term

installation cost is a significant issue, not only for long distance power transmission, but

also for local energy use. As noted above, new pole transformers are required to use Cu

rather than Al to improve efficiency. In the1970’s houses were wired with Al wire rather

than Cu wire to save money in new construction. Unfortunately, there are many safety

problems associated with Al wiring, and the practice has been discontinued.

In order to produce electrical power, the power station must consume another form of energy. In

the US this is dominantly the burning of hydrocarbons, dominated by coal. A diagram of the

primary energy sources for US power plants are shown in the map below from the US

department of energy. Once the power is generated, it needs to be distributed. Power distribution

in the US is divided into regional authorities, some of which include Canada and Mexico. The

regional power authorities are shown in the pack at right, which also shows the power control

centers and connections that are used to redistribute power around the US to provide continuous

power despite changes in supply and demand.

http://www.nerc.com/regional/NERC_Regions_BA.jpg

A grid works very well as a power distribution system because it allows a lot of sharing.

If a power company needs to take a power plant or a transmission tower off line for

maintenance, the other parts of the grid can pick up the slack.

The thing that is so amazing about the power grid is that it cannot store any power

anywhere in the system. At any moment, you have millions of customers consuming

megawatts of power. At that same moment you have dozens of power plants producing

exactly the right amount of power to satisfy all of that demand. And you have all the

transmission and distribution lines sending the power from the power plants to the

consumers.

This system works great, and it can be highly reliable for years at a time. However, there

can be times, particularly when there is high demand, that the interconnected nature of

the grid makes the entire system vulnerable to collapse. Here's how that happens:

Let's say that the grid is running pretty close to its maximum capacity. Something causes

a power plant to suddenly trip off line. The "something" might be anything from a serious

lightning strike to a bearing failure and subsequent fire in a generator. When that plant

disconnects from the grid, the other plants connected to it have to spin up to meet the

demand. If they are all near their maximum capacity, then they cannot handle the extra

load. To prevent themselves from overloading and failing, they will disconnect from the

grid as well. That only makes the problem worse, and dozens of plants eventually

disconnect. That leaves millions of people without power.

The same thing can happen if a big transmission line fails. In 1996 there was a major

blackout in the western U.S. and Canada because the wires of a major transmission line

sagged into some trees and shorted out. When that transmission line failed, all of its load

shifted to neighboring transmission lines. They then overloaded and failed, and the

overload cascaded through the grid.

In nearly every major blackout, the situation is the same. One piece of the system fails,

then the pieces near it cannot handle the increased load caused by the failure, so they fail.

The multiple failures make the problem worse and worse and a large area ends up in the

dark. One solution to the problem would be to build significant amounts of excess

capacity -- extra power plants, extra transmission lines, etc. By having extra capacity, it

would be able to pick up the load at the moment that something else failed. That

approach would work, but it would increase our power bills.

http://people.howstuffworks.com/blackout.htm

http://www.aip.org/tip/INPHFA/vol-9/iss-5/p8.html

The blackout provided an opportunity to measure the pollutants emitted by powerplants since

there was no emission during the blackout. The reduction in emissions was both rapid and

significant.

Electrical power is only one component of our energy use. The chart below shows the original

sources for US energy, the final form in which it is used is shown below. Notice that almost 60%

of the energy is actually lost.