11.3 Ohm’s Law - KWIC Internetmy.kwic.com/~gpguch/files/9chapter11.3.pdfFigure 11.36 Georg Ohm (1789–1854) 11.3 ist9_ch11.qxd 7/21/09 3:18 PM Page 458 Current electricity is the

458 UNIT D The Characteristics of Electricity

Here is a summary of what youwill learn in this section:

• Ohm’s law, V = IR, describesthe relationship betweenpotential difference, current,and resistance.

• In a short circuit, the currentdoes not take the intendedpath back to its source.

• Fuses and circuit breakers aresafety devices.

Ohm’s Law

A Fascination with ElectricityThe circuit boards in the computers you use work because of therelationships between potential difference, current, and resistance(Figure 11.35). These relationships have been understood for about200 years because of the work of Georg Ohm.

Georg Simon Ohm (Fig 11.36) was like any German boy inthe early 1800s. At the local high school, he studied physics,chemistry, math, and philosophy. He spent most of his free timeplaying billiards, ice skating, and dancing with his friends. Noone imagined that one day he would be a famous name inscience.

His journey to discovering a scientific law began aftergraduation when he went to a private school in Switzerland toteach. Here Ohm taught mathematics, but secretly he dreamedof studying with great mathematicians at an importantuniversity.

To achieve his dream, he continued to study mathematics andteach. One day, he was asked to instruct in the electricity labs.This day was a turning point in Georg Ohm’s life. Fascinated byelectricity, he immersed himself in the study of the characteristicsof potential difference, current, and resistance.

Figure 11.35 Potential difference, current, and resistance have the same relationship inmicrocircuits in a computer circuit board like this one as they do in the wiring in homesand offices.

Figure 11.36 Georg Ohm (1789–1854)

11.3

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459Current electricity is the continuous flow of electrons in a closed circuit.

Ohm’s passion and commitment to his studies led to a deepunderstanding of how these different electrical concepts wererelated. Much of what he discovered you have already learned inthis unit. He stated these discoveries in what is today calledOhm’s law.

A law in science is a generalization based on collection ofobservable evidence. It is the conclusion of this evidence and can bedefended by repeating a variety of experiments over many years. Ascientific law becomes accepted by the scientific community as adescription of our natural world.

Ohm’s law established the relationships between potentialdifference (V), current (I), and resistance (R). The symbol forresistance is called the ohm (�) in honour of Georg Ohm’s workin this field.

WORDS MATTER

The symbol “I ” is used for currentbecause it stands for “intensity.”

D21 Quick Lab

Potential Difference, Current, and Resistance

Using the equipment available in your science class,you can investigate the same relationships betweenpotential difference, current, and resistance thatGeorg Ohm did over 200 years ago.

PurposeTo observe how potential difference, current, andresistance are related

Procedure

1. Create a table like the one below to record thedata you will collect. Give your table a title.

2. Connect one resistor into a simple circuit. If youare using a voltmeter and ammeter, connectthese devices as well. Keep your circuit openuntil your teacher has approved your set-up.

3. Close your circuit.

4. Measure and record the voltage across theresistor.

5. Measure and record the current through theresistor.

6. Record the resistance of the resistor you used.

7. Repeat steps 2 to 6.

8. Clean up your work area.

Question

9. Multiply the resistance by the current for each ofthe trials you completed. What can you infer fromyour answers?

Trial Resistance (�)

Current (A)

PotentialDifference (V)

Resistance� Current

1.

2.

• 1.5 V dry cell

• resistors, any values from 15 � to 50 �

• connecting wires

• switch

• multimeter or voltmeter and ammeter

Materials & Equipment

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Potential Difference, Current, and ResistanceGeorg Ohm described how potential difference and current areaffected when one of the values is changed. He realized that thepotential difference (V) in a circuit is equal to the current (I)multiplied by the resistance (R). Ohm’s law states that, as long astemperature stays the same, V = IR (Figure 11.37). In other words:

• the resistance of a conductor remains constant

• the current is directly proportional to the potentialdifference

Table 11.4 and the following examples show how to useOhm’s law to calculate unknown quantities.

Suggested Activities •D23 Inquiry Activity on page 465D24 Inquiry Activity on page 466 Known

Quantity SymbolUnknownQuantity Symbol Unit Equation

Current,resistance

IR potentialdifference

V V V = IR

Potentialdifference,resistance

VR current I A I = VR

Potentialdifference,current

VI resistance R � R = VI

Table 11.4 Ohm’s Law

Example Problem 11.1

A current of 4.0 A flows through a 40-� resistor in a circuit.What is the voltage?

GivenCurrent I = 4.0 AResistance R = 40 �

RequiredVoltage V = ?

Analysis and SolutionThe correct equation is V = IR.Substitute the values and their units, and solve the problem.V = IR

= (4.0 A)(40 �)= 160 V

ParaphraseThe voltage in the circuit is 160 V.

Practice Problems

1. A current of 1.5 A flowsthrough a 30-� resistorthat is connected across abattery. What is thebattery’s voltage?

2. If the resistance of a carheadlight is 15 � and the current through it is0.60 A, what is the voltageacross the headlight?

3. The current in a circuit is0.50 A. The circuit has tworesistors connected inseries: one is 110 � and theother is 130 �. What is thevoltage in the circuit?

VV R

V = IR

I

Figure 11.37 Ohm’s law states thatpotential difference (V) equalscurrent (I) times resistance (R).

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A 30-V battery generates a current through a 15-� resistor.How much current does the battery generate?

GivenVoltage V = 30 VResistance R = 15 �

RequiredCurrent I = ?

Analysis and SolutionThe correct equation is I = V .

R

Substitute the values and their units, and then solve theproblem. I = V

R

= 30 V = 2 A 15 �

ParaphraseA current of 2 A is generated.

Practice Problems

1. A firetruck has asearchlight with aresistance of 60 � that isplaced across a 24-Vbattery. What is thecurrent in this circuit?

2. A bulb of 15-� resistanceis in a circuit powered bya 3-V battery. What is thecurrent in this circuit?

3. What would the currentbe in question 2 if youchanged to a 45-� bulb?


An electric stove is connected to a 240-V outlet. If the currentflowing through the stove is 20 A, what is the resistance of theheating element?

GivenVoltage V = 240 VCurrent I = 20 A

RequiredResistance R = ?

Analysis and SolutionThe correct equation is R = V

I

Substitute the values and their units, and then solve the

problem. R = VI

= 240 V = 12 �20 A

ParaphraseThe resistance of the heating element is 12 �.

Practice Problems

1. A current of 0.75 passesthrough a flashlight bulbthat is connected to a 3.0-V battery. What is thebulb’s resistance?

2. A current of 625 mAruns through a bulb thatis connected to a 120-Vpower supply. What is theresistance of the bulb?

3. A table lamp draws acurrent of 200 mA whenit is connected to a 120-Vsource. What is theresistance for the tablelamp?

.

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During Reading


Ohm’s Law and TemperatureOhm’s law works for most circuits. However, temperature affectsresistance. Generally, resistance is lower when a conductor iscooler. As the temperature increases, resistance increases. Forexample, a filament in an incandescent light bulb often has 10times its normal current flowing through it at the instant it isswitched on. This current heats the filament white-hot in afraction of a second. The huge rise in temperature greatlyincreases the filament’s resistance, which reduces the currentflowing through it. Light bulb filaments sometimes burn outwhen they are switched on because of the sudden temperaturechange and other forces caused by the large initial current.

Short CircuitsSometimes a wire’s insulation breaks down or another problemdevelops that allows electrons to flow through a device along adifferent path than the one intended. The device develops a shortcircuit. A short circuit is an accidental low-resistance connectionbetween two points in a circuit, often causing excess current flow(Figure 11.38). Not only do short circuits mean that yourelectrical device will not work, they can also be dangerous. Theconducting wires can quickly become hot and can start a fire.

One danger from short circuits occurs when a transmissionline has been knocked down in a storm. Without a complete path,the electricity cannot flow. However, if you come in contact withthe wire, the electricity will take a path through your body to theground and seriously injure or kill you. The driver shown inFigure 11.39 is safe as long as he is inside the truck. If he has toleave, he would need to jump free, not step out. He has to jump sohe does not provide a path for the electricity to flow through himto the ground.

There are times when a technician must short out part of acircuit intentionally by connecting a wire across a load in parallel.The low-resistance wire causes the current to flow through itrather than through the higher resistance device. This allows thetechnician to work on the device without interrupting the rest ofthe circuit.

short circuit

Figure 11.38 Current can flow moreeasily through the wire path thanthrough the light bulb. This createsa short circuit, which could bedangerous.

Figure 11.39 The driver should stayin the truck and wait for help.

Definitions in Context

Often, unfamiliar terms aredefined right in the text that youare reading. You don’t need tolook them up in a glossary ordictionary. Look for theboldfaced words, and then findthe definition in the sentenceeither before or after the term.Add words and definitions toyour personal list of terms.

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Electrical SafetyAll electrical appliances present a risk ofelectric shock. Always handle electricalappliances properly and observe all safetyprecautions. Be careful to disconnect the plugbefore handling an appliance. Some electronicdevices, such as computers, retain electriccharge even when they are unplugged (Figure 11.40). This is why many electricaldevices have a “Do Not Open” warningprinted on them. Take the warning seriously,and do not attempt to repair the deviceyourself. Instead, contact a repair technician.

Fuses and Circuit BreakersIn electric circuits in your home,fuses and circuit breakers act as afirst line of defence if something goeswrong. A fuse is a safety device in anelectric circuit that has a metallicconductor with a low melting pointcompared to the circuit’s wires(Figure 11.41). If the current gets too high,the metal in the fuse melts and the currentflow stops. This prevents further problems,such as damage to your electrical componentsor a possible fire. A blown fuse must bephysically replaced as it can work only once.The symbol represents a fuse in acircuit diagram.

A circuit breaker does the same job as afuse except that the wire inside does not melt.Instead, the wire heats up and bends, whichtriggers a spring mechanism that turns off theflow of electricity. Once the breaker hascooled, it can be reset. Older homes andapartment buildings tend to have fuse panels,whereas modern buildings have breakerpanels (Figure 11.42).

Figure 11.40 Some electronic devices, such as this computer,store electrical energy even when the device is not plugged in.

Figure 11.41 Examples of fuses. Anormal current can pass through afuse, but a higher than normalcurrent or short circuit will melt themetal in the fuse.

Figure 11.42 Circuit breakers help prevent electric overloads.

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Figure 11.43 One prong in a three-prongplug carried the current to the load,another prong returns the current to thesource, and the third prong directs thecurrent to the ground in the case of ashort circuit.


Three-Prong PlugAnother safety feature is the three-prong electrical plug shown inFigure 11.43. The third prong of a three-prong electrical plugconnects the device to the ground wire of the building. Theground wire sends any unwanted current flow directly to theground. Instead of electricity travelling to the metal body of thedevice and shocking a person using the device, the current isdirected to the ground.

Ground Fault Circuit InterrupterSome appliances and devices have an added safety feature. Aground fault circuit interrupter (GFCI) or residual currentdevice is a device that detects a change in current and opens thecircuit, stopping current flow (Figure 11.44). For example, if anappliance gets wet while you are handling it and some currentstarts to flow through the water, the GFCI opens the circuit sothere is less chance of injury to you. Remember, it is extremelydangerous to use any electrical device around water, includingradios or televisions.

Figure 11.44 Ground fault circuitinterrupters are part of some electricsockets.

D22

Electrical Safety

Imagine you have just been hired as a consultantby the Electrical Safety Authority of Ontario tohelp create awareness of electrical safety forkindergarten students.

1. Work alone, with a partner, or in a smallgroup to create an electrical safety poster orbrochure that can be shared with akindergarten class. Be sure to chooseelectrical safety points that are relevant toyoung children and to communicate them inan engaging way.

Science, Technology, Society, and the EnvironmentSTSE

Diodes are devices that allowelectric current to flow in onedirection but not in the oppositedirection. Find out how diodes areused in microcircuits and othercircuits. Start your research atScienceSource.

Take It Further

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D23 Inquiry Activity

QuestionHow are potential difference, current, and resistancerelated?

Procedure

1. Set up a data table like the following. Fill in theresistor value for the two resistors you will beusing. Examples below are 100 � and 200 �.Give your table a title.

2. Construct the following circuit using resistor 1and one 1.5 V dry cell (Figure 11.45).

3. Have your teacher approve your circuit, and thenclose the switch. Quickly measure and recordcurrent and voltage. Open the switch.

4. Replace resistor 1 with resistor 2. Repeat step 3.

5. Connect a second 1.5-V dry cell in series with thefirst cell in the circuit. Repeat steps 3 and 4,measuring current and voltage for each resistor.

6. Connect a third 1.5-V dry cell into the circuit.Repeat steps 3 and 4.

7. Connect a fourth 1.5-V dry cell. Repeat steps 3and 4.

8. Calculate your measured resistance for eachresistor using R = V .

I

Analyzing and Interpreting

9. (a) How did your calculated values for resistorscompare with their actual values?

(b) Explain possible reasons for any differencebetween the two values.

10. Compare your data for all resistor 1 trials. Whenvoltage is increased across a resistor, whathappens to the current?

11. Compare your data for all resistor 2 trials. Whenvoltage is increased across the resistor, whathappens to the current?

Skill Practice

12. What would happen to the current values if youused a resistor with double the value of resistor 2?

Forming Conclusions

13. Describe the relationship between potentialdifference, current, and resistance.

Investigating Ohm’s Law

SKILLS YOU WILL USE� Interpreting data/information to

identify patterns or relationships� Drawing conclusions

CAUTION: Disconnect the circuit if the wires or resistorsget hot.

Skills References

A

V Figure 11.45 Construct thiscircuit in step 5.

2, 10

Resistor(�)

Voltage(V)

Current(A)

CalculatedResistance

1.5 V1. 100

2. 200

3.0 V1. 100

2. 200

4.5 V1. 100

2. 200

6.0 V1. 100

2. 200

• four 1.5-V dry cells


• voltmeter, ammeter

• switch

• 2 different resistorsbetween 100 � and300 �


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D24 Inquiry Activity

QuestionDo different materials have different values ofelectrical resistance?

Procedure

1. Make a table for recording your data (Figure11.46). The table should include these headings:Substance, Length Connected (10 cm or 1 cm),Voltage (from step 2), Current, and Resistance. Inthe “Resistance” column, you will calculate theresistance for each observation. Give your table atitle.

2. Use connecting wires to connect each end of a Dcell to a terminal on the voltmeter. Record thevoltmeter reading in your table. Disconnect thevoltmeter.

3. Connect one wire from the D cell to a terminal ofthe ammeter (or current sensor). Attach anotherconnecting wire to the other terminal of theammeter.

4. Clip the free ends of the connecting wires ontothe ends of a 10-cm length of solid graphite.Record the reading on the ammeter.

5. Move the clips on the graphite so that they are 1.0 cm apart. Record any change in the reading.

6. Repeat steps 4 and 5 for the copper wire,Nichrome™ wire, rubber tubing, and the othermaterials.

7. Clean up your work area.

Analyzing and Interpreting

8. Use Ohm’s law to calculate the

resistance for each current recorded in your table.

9. (a) Which substance had the greatest resistance?

(b) Explain any differences in resistance amongthe materials.

10. What was the effect of moving the connectingwires so that the current travelled through ashorter length of the conductor? Explain.

Skill Practice

11. (a) How precise were your measurements?

(b) What sources of error could have affected theaccuracy of your results?

Forming Conclusions

12. Write a summary that answers the question: Dodifferent materials have different values ofelectrical resistance? Use your data to supportyour answer.

VI

R =

Resisting the Flow

SKILLS YOU WILL USE� Justifying conclusions� Identifying sources of error

CAUTION: Open the circuit if the wires or the resistorsget hot.

Skills Reference 2

Figure 11.46 Determining resistance


• D cell and holder

• voltmeter

• ammeter or currentsensor

• 10-cm length of solidgraphite (pencil lead)

• 10-cm length of copperwire

• 10-cm length ofNichrome™ wire

• 10-cm length of rubbertubing

• optional: 10-cm lengths of various othermaterials

• calculator


Key ActivityDI

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Key Concept Review

1. (a) How is current related to potentialdifference in a circuit?

(b) How is current related to resistance in acircuit?

2. What does Ohm’s law state?

3. Copy this table into your notebook, andcomplete the values for potential difference,current, and resistance in an electric circuit.

4. What is each of these meters called?

(a)

(b)

5. What does each meter in question 4measure?

6. Draw labelled circuit diagrams to show howeach meter in question 4 is connected in a:

(a) series circuit

(b) parallel circuit

7. (a) What is a fuse?

(b) What is a fuse used for?

(c) If a fuse melts, does it create an opencircuit, a closed circuit, or a short circuit?

Connect Your Understanding

8. What is the resistance in the circuit shownhere?

9. A 12-� light bulb is in a series circuitpowered by a 6.0-V battery.

(a) What is the current in the circuit?

(b) If you changed the 12-� bulb to a 24-�bulb, what current would be drawnfrom the battery?

10. (a) If a 36-� bulb is added in series in thecircuit in question 9(a), what is thecurrent in the circuit?

(b) What is the potential difference acrosseach bulb?

11. In a circuit where voltage is kept constant,state what happens to current if resistance is:

(a) doubled

(b) quadrupled

12. (a) Why is a ground fault circuit interrupternecessary for electrical devices that areused around water?

(b) List three devices that should include aground fault circuit interrupter.

Reflection

13. What questions about electricity would youlike to have answered?

For more questions, go to ScienceSource.

3.0 A

6.0 V

V I R

0.5 V 50 �

20 A 100 �

6.0 V 4.0 A

Potential Difference, Current, and Resistance

Question 8

11.3 CHECK and REFLECT

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CAREERS in ScienceInvestigating

Great CANADIANS in Science Max Donelan

Award-winning Canadian scientist Dr. MaxDonelan walks down many different scientificpaths. In fact, walking is something he would liketo help more people be able to do. While mosthealthy people find walking a simple matter, manyindividuals who suffer from paralysis due to astroke find that any kind of walking can be onestep too far.

A stroke is a medical condition that occurs whena blood vessel in the brain leaks. This leakage ofblood causes brain and nerve damage. Forexample, the damage can make it difficult to usethe muscles on one side of the body while theother side is not affected at all. A person who hashad a stroke may be able to walk but may find thathe or she needs to use much more energy than ahealthy person to do the same amount of walking.Dr. Donelan is working to find out why.

Dr. Donelan and his colleagues at Simon FraserUniversity in British Columbia are studying thescience behind the way healthy people walk. Theywill use the results of their studies to designdevices and strategies to help patients use energyefficiently and regain as much mobility as possible.

Even healthy people may benefit from hisresearch. In studying the energy requirementsinvolved with walking, Dr. Donelan’s team hascome up with a device that is able to captureenergy that is generated when a person walks(Figure 11.47). His device assists the movementof leg muscles while generating electricity at thesame time. This is called “harvesting” energy.Harvesting usually refers to gathering in crops likegrains or vegetables when they are ripe. In thiscase, the crop is energy!

Dr. Donelan’s team is working to design anenergy harvester that is lightweight, slim, andbarely noticeable when worn. Being able toproduce your own electricity is useful to people inlocations where a constant electrical power supplyis not available, such as hikers and emergencycrews. In the field of energy efficiency, Dr. Donelanis clearly a step ahead.

Questions

1. What does it mean to “harvest” energy?

2. ScienceSource Research to find out whatpossible applications a human-poweredenergy harvesting device could have in oneof the following fields:

• medicine

• public safety

• the military

Figure 11.47 Dr. Donelan watches his device in use. It isstrapped to the knee of this walker. For every minute ofwalking you do, the device harvests enough electrical energyto power a cell phone for about 30 minutes.

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Science in My FUTURE

Are you ready for a career challenge? Supposeyour job description included climbing a telephonepole at night during a snowstorm when the powerwas out — in fact, you would be climbing the polebecause the power was out?

Electrical energy is an essential part of oursociety, and waiting for a storm to end is notusually an option when the power grid goes down.Line installers and repairers are sent out oftenduring a summer lightning storm or a winterfreeze-up to keep electricity flowing to homes andbusinesses (Figure 11.48).

As a line installer, you would do more thanmake sure the lines were properly connected andrepaired. Line installing and repair includesworking with electronics and telecommunications,such as telephone, Internet, and cable televisionlines. New construction, which involves putting uppoles or burying cables, means you are likely touse a variety of equipment, such as diggers,trench makers and tunnelling machines. Althoughmachines would help you lift and carry, you wouldneed to be strong and physically fit. Climbing tohigh places and working with high voltage carry adefinite risk, so an attitude of being careful andworking safely is essential. You might set upservice in homes for customers, so good peopleskills are also an asset.

For a career as a line installer and repairer, highschool completion that includes algebra andtrigonometry is an asset, as are the kinds ofpractical skills learned in shop classes.Community colleges and technical schools oftenoffer programs in electricity, electronics, andtelecommunications. These programs frequentlypartner with companies in the local community tooffer hands-on field work.

Figure 11.48 A line installer needs a good understanding ofelectrical safety.

Line Installers and Repairers

Even our increasingly wirelessly connectedworld, we will still need tough, smart, cautious,and strong individuals to keep the grid workingproperly.

Questions

1. List four qualities that would be an asset for aperson interested in work as a line installer orrepairer.

2. ScienceSource There are many careersrelated to electrical technologies, includingelectricians, power plant operators, and radioand telecommunications equipmentinstallers and repairers. Select one of theseor another related field, and summarize whatthe job involves, the education and trainingneeded, and one aspect of the job that isparticularly interesting to you.

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Documents

11.3 Ohm’s Law - KWIC Internetmy.kwic.com/~gpguch/files/9chapter11.3.pdfFigure 11.36 Georg Ohm (1789–1854) 11.3 ist9_ch11.qxd 7/21/09 3:18 PM Page 458 Current electricity is the