Physics of Circuits

1
Physics of Circuits

• Created for BW Physics
• Middle School Science Teachers
• By
• Dick Heckathorn
• 23 April 2K 8

2
Equipment

• 1. Meter
• 2. Resistors
• 3. Battery
• 4. Connecting Wire

3
Table of Contents

• 4 A. Finding Total or Equivalent Resistance of
  Resistors in Series
• 12 B. Finding Total or Equivalent Resistance of
  Resistors in Parallel
• 19 C. Circuit Analysis One Resistor
• 29 D. Circuit Analysis Two Resistors Connected
  in Series
• 38 E. Circuit Analysis Two Resistors Connected
  in Parallel
• 49 Final Summary with Some Problems
• 64 Connecting a 3-Way Switch

4
A. Finding Total or Equivalent Resistanceof
resistors connectedinSeries
5

• 1. Measure and record the resistance of three
  resistors.

_______ _______ _______
6

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

7

• 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.

8

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

R1 R3
R2 R3
9

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

_____________
10

• 6. Does your rule for three resistors connected
  in series the same as for two resistors connected
  in series?
• Yes ___ No ___

11

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

Remember this is for ONLY resistors in series!
12
B. Finding Total or Equivalent Resistance of
Resistors in Parallel
13

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

14

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

15

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

16

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

17

• 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 ___

18

• 6. The rule is

Remember this is ONLY for resistors in parallel!
19
C. Circuit Analysis One Resistor
20
1. Measure the value of a resistor. R ___ Set
the ammeter to its greatest value. Then construct
the following circuit.
21
Measure and record
I
R
Voltage VB
Voltage VA
Current I
Voltage VR
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Conclusion(s)
I
R
I?
VB, I, and R?
VB, I, and R?
Compare VB with VA and VR and
Compare VB with VA and VR and
23

• 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.
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8. Remove Ammeter
R
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9. Connect and measure the voltage across the
battery and then the resistor. Record the values.
R
VR _______
VB _______
26
Conclusion(s)?
R
How do VB and VR compare?
27
10. Calculate
How do they compare?
28

• 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.

29
D. Circuit AnalysisTwo ResistorsConnected in
Series
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1. Measure the value of two resistors. R1
_________ R2 _________ Then construct
the following circuit.
31
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 _______
VR! _______
VR2 _______
33

• 4. How does VB compare to VR1 and VR2?
• 5. Calculate VR1/R1 and VR2/R2
• ______ ______
• What do these values compare to?

34
5. Calculate both VR1/R1 and VR2/R2.
How do they compare?
What do these values compare to?
35

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

36
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 (V1V2) lost
in the components connected in series.
37
Conclusion(s)
Compare VB with VA and VR
Compare VB, I, and R1 R2?
38
E. Circuit AnalysisTwo ResistorsConnected in
Parallel
39
1. Measure the value of both resistor. R1
_______ R2 _______ Then construct the
following circuit.
40
2. Record the value of the current
IT ________
41
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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Measure and record both currents.
IR1 ____________ IR2 ____________
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4. How is the does the current through each
meter, IR1 and IR2 compare to the total current
IT?
IT _______ IR1 _______ IR2 _______
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5. Remove all ammeters which will give you the
following circuit.
45
6. Measure and record the voltage across the
battery VB, and the voltage across the two
resistors VR1 and VR2
VB _______ VR1 _______ VR2 _______
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• 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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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.

49
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
R3
R2
R1
V1
V3
V2
VT
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ResistanceinSeries
12 O, 25 O, and 42 O in series
The equivalent resistance is
79 O
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Resistance in Series
Three 30-O light bulbs and two 20-O
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-O
bulbs the 2nd has twelve 3-O bulbs The
equivalent resistance is .
68 ohms
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Resistance in Series
Find the value of the unknown resistance in the
following
a 20-O, a 18-O, and an unknown resistor are
connected in series to give an equivalent
resistance of 64-O
26 ohms
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Parallel Circuit
R1
I1
V1
R2
I2
IT
V2
VT
R3
I3
V3
58
Resistance in Parallel
Find the equivalent resistance when a 4-O and
an 8-O bulb are connected in parallel.
2.7 ohm
59
Resistance in Parallel
Find the equivalent resistance when a 16-O and an
8-O bulb are connected in parallel.
5.3 ohm
60
Resistance in Parallel
Find the equivalent resistance when a 20-O, a 10-
O and a 5-O bulb are connected in parallel.
2.9 ohm
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Resistance in Parallel
What resistance would have to be added in
parallel with a 40- O hair dryer to reduce the
equivalent resistance to 8- O?
10 ohm
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Resistance in Parallel
Find the equivalent resistance of two, three,
four, and five 60-O bulb are connected in
parallel.
30 O
12 O
20 O
15 O
Is there a simple relationship for the equivalent
resistance of n resistors in parallel?
R/n
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Thats all folks!
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