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Unit Three:Ohm’s Law

John Elberfeld

JElberfeld@itt-tech.edu

WWW.J-Elberfeld.com

ET115 DC Electronics

ScheduleSchedule

Unit Unit Topic Topic Chpt LabsChpt Labs1.1. Quantities, Units, SafetyQuantities, Units, Safety 11 2 (13)2 (13)2.2. Voltage, Current, ResistanceVoltage, Current, Resistance 22 3 + 163 + 163.3. Ohm’s LawOhm’s Law 33 5 (35)5 (35)4.4. Energy and PowerEnergy and Power 33 6 (41)6 (41)

5.5. Series CircuitsSeries Circuits Exam IExam I 44 7 (49)7 (49)

6.6. Parallel CircuitsParallel Circuits 55 9 (65)9 (65)

7.7. Series-Parallel CircuitsSeries-Parallel Circuits 66 10 (75)10 (75)

8.8. Thevenin’s, Power Thevenin’s, Power Exam 2Exam 2 66 19 (133)19 (133)

9.9. Superposition Theorem Superposition Theorem 66 11 (81)11 (81)

10.10. Magnetism & Magnetic DevicesMagnetism & Magnetic Devices 77 Lab Final Lab Final 11.11. Course Review and Course Review and Final ExamFinal Exam

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Unit 3 Objectives - IUnit 3 Objectives - I

• Describe the relationship among voltage, Describe the relationship among voltage, current, and resistance.current, and resistance.

• Given two of the three variables in Ohm’s Given two of the three variables in Ohm’s Law, solve for the remaining quantity.Law, solve for the remaining quantity.

• Solve Ohm’s Law problems using metric Solve Ohm’s Law problems using metric prefixes.prefixes.

• Construct basic DC circuits on a Construct basic DC circuits on a protoboard.protoboard.

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Unit 3 Objectives – IIUnit 3 Objectives – II

• Use a digital multimeter (DMM) to measure Use a digital multimeter (DMM) to measure a predetermined low voltage on a power a predetermined low voltage on a power supply.supply.

• Measure resistances and voltages in a DC Measure resistances and voltages in a DC circuit using a DMM.circuit using a DMM.

• Explain the Multisim workbench and show Explain the Multisim workbench and show how to construct a basic circuit.how to construct a basic circuit.

• Test circuits by connecting simulated Test circuits by connecting simulated instruments in Multisiminstruments in Multisim

Reading AssignmentReading Assignment

• Read and study Read and study

• Chapter 3: Ohm’s Law Chapter 3: Ohm’s Law Pages 71-80Pages 71-80

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Lab AssignmentLab Assignment

• Lab Experiment 5:Lab Experiment 5:

• Ohm’s Law Pages 35-38Ohm’s Law Pages 35-38

• Complete all measurements, graphs, Complete all measurements, graphs, and questions and turn in your lab and questions and turn in your lab before leaving the roombefore leaving the room

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Written AssignmentsWritten Assignments

• Answer all questions on the Answer all questions on the homework handouthomework handout

• Be prepared for a quiz on questions Be prepared for a quiz on questions similar to those on the homework.similar to those on the homework.

• If there are any calculations, you must If there are any calculations, you must show ALL your work for credit:show ALL your work for credit:– Write down the formulaWrite down the formula– Show numbers in the formulaShow numbers in the formula– Circle answer with the proper unitsCircle answer with the proper units

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Ohms LawOhms Law

• MEMORIZE: V = I RMEMORIZE: V = I R• Ohm’s LawOhm’s Law• If you increase the voltage, you If you increase the voltage, you

increase the current proportionallyincrease the current proportionally– 3 times the voltage gives you three 3 times the voltage gives you three

times the currenttimes the current– Resistance (ohms) is the proportionality Resistance (ohms) is the proportionality

constant and depends on the atomic constant and depends on the atomic structure of the material conducting the structure of the material conducting the currentcurrent

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Experimental ResultsExperimental Results

Current (x) Voltage (y)

0 A 0 V

2 A 6 V

4 A 12 V

6 A 18 V

8 A 24 V

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Graph of Data

x

I – Current in Amps

V

Voltage

x

x

x

x

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ReasoningReasoning

• Ohms Law: V = I ROhms Law: V = I R• High voltage produces high current for a High voltage produces high current for a

given resistancegiven resistance• Low voltage produces low current for a Low voltage produces low current for a

given resistancegiven resistance• For a given voltage, a high resistance For a given voltage, a high resistance

produces a low currentproduces a low current• For a given voltage, a low resistance For a given voltage, a low resistance

produces a high currentproduces a high current

V = I R

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Electronic CircuitElectronic Circuit

• A battery with the voltage V pushes a A battery with the voltage V pushes a current I through a resistor Rcurrent I through a resistor R

V = I R

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Ohm’s LawOhm’s Law

• This is the BIG IDEA for the day (year)!This is the BIG IDEA for the day (year)!

• V = I RV = I R• What if we divide both sides by R?What if we divide both sides by R?• VV = = I RI R

R R R R• But R/R = 1, so we don’t need to write it But R/R = 1, so we don’t need to write it

down:down:• I = I = VV I = V / RI = V / R

RR

V = I R

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Ohm’s LawOhm’s Law

• V = I RV = I R• What if we divide both sides by I?What if we divide both sides by I?

• VV = = I RI R I I I I

• But I / I = 1, so we don’t need to write But I / I = 1, so we don’t need to write it down:it down:

• R = R = VV R = V / IR = V / I I I

V = I R

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Ohm’s LawOhm’s Law

• Memorize: V = I RMemorize: V = I R

• Use algebra to find:Use algebra to find:

• I = V / RI = V / R

• R = V / IR = V / I

• If you can, learn all three variations, If you can, learn all three variations, but you can get by if you memorize:but you can get by if you memorize:

V = I RV = I R

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PracticePractice

•V = I RV = I R• What voltage (V) is needed to push a What voltage (V) is needed to push a

current of 2 Amperes (I) through a current of 2 Amperes (I) through a resistance of 18 Ohms (R) ?resistance of 18 Ohms (R) ?

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PracticePractice

•V = I RV = I R• What voltage (V) is needed to push a What voltage (V) is needed to push a

current of 2 Amperes (I) through a current of 2 Amperes (I) through a resistance of 18 Ohms (R) ?resistance of 18 Ohms (R) ?

• V = I RV = I R

• V = 2 A x 18 V = 2 A x 18 ΩΩ

• V = 36 VV = 36 V

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ExamplesExamples• Ohms Law: V = I R k = 10Ohms Law: V = I R k = 1033 μ = 10μ = 10-6-6

• How much voltage must be connected How much voltage must be connected across a 1.2 k across a 1.2 k Ω resistor to cause 575 Ω resistor to cause 575 μA of current to flow?μA of current to flow?

• V = I RV = I R

? V 1.2k Ω

575 μA

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ExamplesExamples• Ohms Law: V = I R k = 10Ohms Law: V = I R k = 1033 μ = 10μ = 10-6-6

• How much voltage must be connected How much voltage must be connected across a 1.2 k across a 1.2 k Ω resistor to cause 575 Ω resistor to cause 575 μA of current to flow?μA of current to flow?

• V = I RV = I R

• V = 575 μA V = 575 μA 1.2 k 1.2 k Ω Ω

• V = .69V = 690 x 10V = .69V = 690 x 10-3-3V = 690 mVV = 690 mV

? V 1.2k Ω

575 μA

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ExamplesExamples

• Ohms Law: V = I ROhms Law: V = I R

• How much current flow through a 25 How much current flow through a 25 Ω resistor with 10 V across it?Ω resistor with 10 V across it?

• V = I RV = I R I = V / RI = V / R

10 V 25 Ω

103=k10-3 = m10-6 = μ

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ExamplesExamples

• Ohms Law: V = I ROhms Law: V = I R

• How much current flow through a 25 How much current flow through a 25 Ω resistor with 10 V across it?Ω resistor with 10 V across it?

• V = I RV = I R I = V / RI = V / R

• 10 V = I 25 Ω10 V = I 25 Ω

• I = 10 V / 25 ΩI = 10 V / 25 Ω

• I = .4 A or 400 x 10I = .4 A or 400 x 10-3-3A = 400 mAA = 400 mA

10 V 25 Ω

103=k10-3 = m10-6 = μ

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ExamplesExamples

• Ohms Law: V = I R Ohms Law: V = I R • If a certain resistor allows 250 mA to If a certain resistor allows 250 mA to

flow when 35 V are across it, what is flow when 35 V are across it, what is the resistance?the resistance?

• V = I RV = I R R = V / IR = V / I

35 V 250 mA

103=k10-3 = m10-6 = μ

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ExamplesExamples

• Ohms Law: V = I R Ohms Law: V = I R • If a certain resistor allows 250 mA to If a certain resistor allows 250 mA to

flow when 35 V are across it, what is flow when 35 V are across it, what is the resistance?the resistance?

• V = I RV = I R R = V / IR = V / I• 35 V = 250 mA R35 V = 250 mA R• R = 35 V / 250 maR = 35 V / 250 ma• R = 140 ΩR = 140 Ω

35 V 250 mA

103=k10-3 = m10-6 = μ

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ExamplesExamples

• Ohms Law: V = I ROhms Law: V = I R

• How much current flow through a How much current flow through a 3.3k 3.3k Ω resistor with 4.5 mV across it?Ω resistor with 4.5 mV across it?

• V = I RV = I R I = V / RI = V / R

4.5 mV 3.3k Ω

103=k10-3 = m10-6 = μ

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ExamplesExamples

• Ohms Law: V = I ROhms Law: V = I R

• How much current flow through a How much current flow through a 3.3k 3.3k Ω resistor with 4.5 mV across it?Ω resistor with 4.5 mV across it?

• V = I RV = I R I = V / RI = V / R

• 4.5 mV = I 3.3k Ω4.5 mV = I 3.3k Ω

• I = 4.5 mV / 3.3k ΩI = 4.5 mV / 3.3k Ω

• I = 1.36 μ AI = 1.36 μ A

4.5 mV 3.3k Ω

103=k10-3 = m10-6 = μ

26 DIRECT AND INVERSE DIRECT AND INVERSE RELATIONSHIPSRELATIONSHIPS

• I = I = VV R R

27 DIRECT AND INVERSE DIRECT AND INVERSE RELATIONSHIPSRELATIONSHIPS

• I = I = VV R R

And Still More PracticeAnd Still More Practice

V = I R I = V / R R = V / I

1.6 mA 2.2 kΩ

250 μA 1.0 kΩ

500 mA 1.5 MΩ

850 μA 10 MΩ

75 μA 47 Ω

3 mA 27 kΩ

5 μA 100 MΩ

2.5 A 47 Ω

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PracticePractice

•V = I RV = I R• What current (I) flows through a What current (I) flows through a

resistance of 8 ohms when the resistance of 8 ohms when the resistor is connect to a 24 volt resistor is connect to a 24 volt battery? battery?

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PracticePractice

• What current (I) flows through a What current (I) flows through a resistance of 8 ohms when the resistance of 8 ohms when the resistor is connect to a 24 volt resistor is connect to a 24 volt battery? battery?

• V = I RV = I R I = V / RI = V / R

• 24 V = I x 8 24 V = I x 8 ΩΩ I = 24 V / I = 24 V / 8 8 ΩΩ

• I = 24 V / 8 I = 24 V / 8 ΩΩ I = 3 AI = 3 A

• I = 3 AI = 3 A

V = I R

And Still More PracticeAnd Still More Practice

V = I R I = V / R R = V / I

40 V 68 kΩ

1 kV 2 kΩ

66 kV 10 MΩ

12 V 10 Ω

25 V 10 kΩ

5 V 2.2 MΩ

15 V 1.5 kΩ

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PracticePractice

• What size resistor allows 2 amperes What size resistor allows 2 amperes of current through it when it is of current through it when it is connected to a 10 Volt power connected to a 10 Volt power supply?supply?

V = I R

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PracticePractice

• What size resistor allows 2 amperes What size resistor allows 2 amperes of current through it when it is of current through it when it is connected to a 10 Volt power connected to a 10 Volt power supply?supply?

• V = I RV = I R R = V / IR = V / I

• 10 V = 2 A x R10 V = 2 A x R R = 10 V / 2 A R = 10 V / 2 A

• R = 10 V / 2 A R = 10 V / 2 A R = 5 R = 5 ΩΩ

• R = 5 R = 5 ΩΩ

V = I R

And Still More PracticeAnd Still More Practice

V = I R I = V / R R = V / I

500 V 250 mA

50 V 500 μA

1 kV 1 mA

6 V 2 mA

8 V 2 A

12 V 4 mA

39 V 150 μA

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Lab 5 - Ohm’s LawLab 5 - Ohm’s Law

• Ohm’s Law describes the Ohm’s Law describes the relationship among voltage, current, relationship among voltage, current, and resistance – it does not control and resistance – it does not control it!it!

• In lab, you will prove to yourself that In lab, you will prove to yourself that Ohm’s Law applies to circuitsOhm’s Law applies to circuits

• Use the special handout to organize Use the special handout to organize your informationyour information

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Select and Measure ResistorsSelect and Measure Resistors

• Your resistors can off by +/- 5% from Your resistors can off by +/- 5% from the marked valuethe marked value

• You must measure as accurately as You must measure as accurately as possible the real resistance used in possible the real resistance used in your experimentyour experiment

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Use TWO metersUse TWO meters

• Use TWO DMMs in your experimentUse TWO DMMs in your experiment• Record as many digits as possible for Record as many digits as possible for

both voltage and currentboth voltage and current

• You must BREAK the circuit to measure You must BREAK the circuit to measure currentcurrent

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A

V

Plot Your PointsPlot Your Points

• Your lab handout says to plot I along Your lab handout says to plot I along the x axis and V along the y axisthe x axis and V along the y axis

• The slope is The slope is ΔΔy / y / ΔΔx = x = ΔΔV/ V/ ΔΔI I

• Based on Ohm’s Law, R = V / I, just Based on Ohm’s Law, R = V / I, just like the slopelike the slope

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Lab 4 – Voltage MeasurementLab 4 – Voltage Measurement

1. Select the correct voltage mode (ac or dc).1. Select the correct voltage mode (ac or dc).

2. Select range higher than expected 2. Select range higher than expected voltage.voltage.

3. Connect the meter across the points. Red, 3. Connect the meter across the points. Red, positive (+), positive (+), Black, Black, common (–)common (–)

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Next StepsNext Steps

• 4. Reduce the range setting until the 4. Reduce the range setting until the reading failsreading fails

• 5. Increase the range setting one 5. Increase the range setting one step and record all the numbers, with step and record all the numbers, with the proper units, shown on the meterthe proper units, shown on the meter

• 34.67 mV, for example34.67 mV, for example

Voltage NotationVoltage Notation

• Voltage is always the difference Voltage is always the difference between TWO points.between TWO points.

• Measure VMeasure VBC BC by attaching the RED by attaching the RED

lead to B and the BLACK lead to Clead to B and the BLACK lead to C

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A B

CD

V

VoltageVoltage

• If only one letter is given, attach the If only one letter is given, attach the RED lead to that letter, and the RED lead to that letter, and the BLACK lead to the reference point or BLACK lead to the reference point or ground.ground.

• If D is your reference point, VIf D is your reference point, VBB is: is:

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A B

CD V

Voltage DifferencesVoltage Differences

• If D is your reference point, thenIf D is your reference point, then

• VVBB is really V is really VBDBD

• VVCC is really V is really VCDCD

• Electrically, thenElectrically, then

• VVBCBC = V = VBDBD - V - VCDCD

• Voltage is the difference between two Voltage is the difference between two pointspoints

• Choosing a different reference point does Choosing a different reference point does NOT change the real voltageNOT change the real voltage

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Unit 3 SummaryUnit 3 Summary

1. Ohm’s Law1. Ohm’s Law

2. Solving for voltage, current, or resistance 2. Solving for voltage, current, or resistance in a one-load circuitin a one-load circuit

3. Ohm’s Law using metric prefixes3. Ohm’s Law using metric prefixes