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Physics of Circuits

Created for BW PhysicsMiddle School Science Teachers

ByDick Heckathorn23 April 2K + 8

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Equipment

1. Meter

2. Resistors

3. Battery

4. Connecting Wire

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Table of Contents

4A. Finding Total or Equivalent Resistance of Resistors in Series12B. Finding Total or Equivalent Resistance of Resistors in Parallel19C. Circuit Analysis One Resistor 29D. Circuit Analysis Two Resistors Connected in Series38E. Circuit Analysis Two Resistors Connected in Parallel49 Final Summary with Some Problems64 Connecting a 3-Way Switch

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A. Finding Total or Equivalent Resistance

of resistors connectedin

Series

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1. Measure and record the resistance of three resistors.

_______ _______ _______

R2 R3R1

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R2 + R_______

2. Connect two of the resistors end to end (in series) and measure the resistance across each pair.

R1 + R2

_______R1 + R3

_______

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3. A new resistor equal to the sum of the two resistors can replace the two resistors and has the same effect in a circuit as the two resistors.

We call the sum, an equivalent resistance or a total resistance.

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4. Develop a rule from which you can predict the equivalent resistance of two resistors in series.

R1 + R2 R1 + R3

R2 + R3

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5. Connect all three resistors end to end and measure the resistance across all three.

R1 + R2 + R3

_____________

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6. Does your rule for three resistors connected in series the same as for two resistors connected in series?

Yes ___ No ___

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7. Your instructor hopes that you found the following to be true.

Remember this is for

ONLY resistors in series!

......321 RRRRT

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B. Finding Total or Equivalent Resistance of Resistors in

Parallel

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1. Record the resistance of the three resistors that you measured before.

R1

_________

R2

_________

R3

_________

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2. Connect two of the resistors as shown (in parallel) and measure the resistance across each end.

R1 : R2

_________

R1 : R3

_________

R2 : R3

_________

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3. Develop a rule from which can predict the equivalent resistance of two resistors in parallel?

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4. Connect all three resistors as shown, then measure the resistance across all three.

R1 : R2 : R3

____________

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5. Is the rule for finding the equivalent resistance of three resistors connected in parallel the same for finding the equivalent resistance of two resistors connected in parallel?

Yes ___ No ___

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6. The rule is:

Remember this is ONLY for

resistors in parallel!

......1111

321

RRRRT

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C. Circuit Analysis One Resistor

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A

R

1. Measure the value of a resistor. R = ___ Set the ammeter to its greatest value. Then construct the following circuit.

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VRVB

Measure and record:

A

Current I

I

R

Voltage VR Voltage VB

VA

Voltage VA

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VA

VRVB

Conclusion(s)

A

Compare VB with VA and VR and

I

R

VB, I, and R?

I?

Compare VB with VA and VR and VB, I, and R?

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6. Divide the voltage (VB) by the resistance (R).

7. How does VB/R compare to the measured current?

Be sure to keep track of units.

____________________toCompares

__________R

VB

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VRVB

8. Remove Ammeter

R

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VRVB R

VB = _______ VR = _______

9. Connect and measure the voltage across the battery and then the resistor. Record the values.

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VRVB

Conclusion(s)?

R

How do VB and VR compare?

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10. Calculate:

__________R

V__________

R

V RR 2

2

1

1

How do they compare?

____________________tocomparesThey

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11. What does your instructor say about this?

Your instructor says that VB and VR should be the same as the energy per charge given to the electrons by the battery VB and then removed by the resistor VR.

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D. Circuit AnalysisTwo Resistors

Connected in Series

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1. Measure the value of two resistors.

R1 = _________ R2 = _________

Then construct the following circuit.

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A

R1

R2

2. Measure and record the current.

I = ____________

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3. Measure and record the voltage across the battery and both of the resistances.

VB = _______

VB

V1

V2

AI

R1

R2

VR! = _______ VR2 = _______

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4. How does VB compare to VR1 and VR2?

5. Calculate VR1/R1 and VR2/R2

______ ______

What do these values compare to?

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5. Calculate both VR1/R1 and VR2/R2.

__________R

V__________

R

V RR 2

2

1

1

What do these values compare to?

How do they compare?

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6. Write a conclusion about the current and voltage in a circuit when two resistors are connected in series with the battery.

21

21

RRB

RRT

VVV

III

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7. What does your instructor say about this?

Resistance in Series

1. Current (I) in the circuit is everywhere the same.

2. Potential difference (VB) supplied by the battery equals the sum of the potential difference (V1+V2) lost in the components connected in series.

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E. Circuit AnalysisTwo Resistors

Connected in Parallel

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1. Measure the value of both resistor.

R1 = _______ R2 = _______

Then construct the following circuit.

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AI

R1 R2

2. Record the value of the current

IT = ________

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A2A1

R1 R2

I1 I2

3. If you have access to two meters, create the circuit below and measure the current through both resistors. Otherwise, hook up A1 measure the current I1 and then repeat for A2.

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A2A1

R1 R2

I1 I2

IR1 = ____________ IR2 = ____________

Measure and record both currents.

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AR2A1

R1 R2

IR1 IR2

IT = _______ IR1 = _______ IR2 = _______

4. How is the does the current through each meter, IR1 and IR2 compare to the total current IT?

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5. Remove all ammeters which will give you the following circuit.

R1 R2

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6. Measure and record the voltage across the battery VB, and the voltage across the two resistors VR1 and VR2

VB _______ VR1 _______ VR2 _______

VB

VR1 VR2R1 R2

46?relatedtheyareHow

?representvaluesthedoWhat

______R

V______

R

V______

R

V

R

R

R

R

T

B 2

2

1

1

7. How is the voltage of the battery VB related to the voltage through each resistor VR1 and VR2?

VB _______ VR1 _______ VR2 _______

Calculate the following:

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11. Write a conclusion about the current and voltage in a circuit where 2 resistors are connected in parallel with the battery.

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21

RRB

RRT

VVV

III

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Summary

1. Current (I) from the battery equals the sum of the currents (I1 + I2) through the separate resistances.

2. Potential difference (VB) supplied by the battery equals the potential difference (V1 = V2) lost in the resistances connected in parallel.

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Final Summarywith some problems

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Summary

What governs the amount of electric potential energy an electron will lose in each load?

The conservation of energy. The amount gained is equal to the sum of the total energy lost.

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Summary

What governs the number of electrons that will take each path?

The conservation of charge. There is no gain or loss of electrons nor any accumulation at any point.

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Series Circuit

321T I I I I

321T V V V V

RIV

R1 R2 R3

VTV1 V2 V3

332211 RIRIRIRI TT

321 RRRRT

onConservatiEnergy

onConservatieCharg

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Resistancein

Series

321 RRRRT

12 Ω, 25 Ω, and 42 Ω in series

The equivalent resistance is 79 Ω

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Resistance in Series

Three 30-Ω light bulbs and two 20-Ω heating elements

connected in series

The equivalent resistance is ….

130 ohms

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Resistance in Series

two strings of Christmas tree lights connected in series, if the

1st string has eight 4-Ω bulbs & the 2nd has twelve 3-Ω bulbs

The equivalent resistance is ….

68 ohms

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Resistance in Series

a 20-Ω, a 18-Ω, and an unknown resistor are connected in series to give

an equivalent resistance of 64-Ω

26 ohms

Find the value of the unknown resistance in the following:

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Parallel Circuit

onConservatieCharg 321T I I I I

R

VI

R1

R2

R3

T

T

R

V

1

1

R

V

2

2

R

V

3

3

R

V

TR

1

1

1

R 2

1

R

3

1

R

321T V V V V onConservatiEnergy

V1

V2

V3

VT

I1

I2

I3

IT

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321

1111

RRRRT

Find the equivalent resistance when a 4-Ω and an 8-Ω bulb are

connected in parallel.

2.7 ohm

Resistance in Parallel

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5.3 ohm

Resistance in Parallel

Find the equivalent resistance when a 16-Ω and an 8-Ω bulb are connected in parallel.

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2.9 ohm

Resistance in Parallel

Find the equivalent resistance when a 20-Ω, a 10- Ω and a 5-Ω bulb are connected in parallel.

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What resistance would have to be added in parallel with a 40- Ω hair dryer to reduce the equivalent resistance to 8- Ω?

10 ohm

Resistance in Parallel

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30 Ω

Resistance in Parallel

Find the equivalent resistance of two, three, four, and five 60-Ω bulb are connected in parallel.

20 Ω 15 Ω 12 Ω

Is there a simple relationship for the equivalent resistance of ‘n’ resistors in parallel? R/n

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That’s all folks!

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