Transcript Physics of Circuits

Physics of Circuits
Created for BW Physics
Middle School Science Teachers
By
Dick Heckathorn
23 April 2K + 8
1
Equipment
1.
2.
3.
4.
Meter
Resistors
Battery
Connecting Wire
2
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
3
A. Finding Total or Equivalent
Resistance
of resistors connected
in
Series
4
1. Measure and record the resistance of
three resistors.
R1
_______
R2
_______
R3
_______
5
2. Connect two of the resistors end to end
(in series) and measure the resistance
across each pair.
R1 + R 2
R1 + R 3
_______
_______
R2 + R
_______
6
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.
7
4. Develop a rule from which you can
predict the equivalent resistance of two
resistors in series.
R1 + R 2
R1 + R 3
R2 + R 3
8
5. Connect all three resistors end to end and
measure the resistance across all three.
R 1 + R2 + R 3
_____________
9
6. Does your rule for three resistors
connected in series the same as for two
resistors connected in series?
Yes ___ No ___
10
7. Your instructor hopes that you found
the following to be true.
RT  R1  R2  R3  ......
Remember this is for
ONLY resistors in series!
11
B. Finding Total or Equivalent
Resistance of Resistors in
Parallel
12
1. Record the resistance of the three
resistors that you measured before.
R1
_________
R2
R3
_________ _________
13
2. Connect two of the resistors as shown
(in parallel) and measure the resistance
across each end.
R1 : R2
R1 : R3
R2 : R3
_________
_________
_________
14
3. Develop a rule from which can
predict the equivalent resistance
of two resistors in parallel?
15
4. Connect all three resistors as shown,
then measure the resistance across all
three.
R1 : R2 : R3
____________
16
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 ___
17
6. The rule is:
1
1 1
1
    ......
RT R1 R2 R3
Remember this is ONLY for
resistors in parallel!
18
C. Circuit Analysis
One Resistor
19
1. Measure the value of a resistor. R = ___
Set the ammeter to its greatest value.
Then construct the following circuit.
A
R
20
Measure and record:
A
I
VA
VB
R
VR
Current I Voltage VR Voltage VA Voltage VB
21
Conclusion(s)
A
I
VA
VB
R
VR
I?
Compare VB with VA and VR and VB, I, and R?
22
6. Divide the voltage (VB) by the resistance
(R).
VB
 __________
R
Compares to ____________________
7. How does VB/R compare to the measured
current?
Be sure to keep track of units.
23
8. Remove Ammeter
VB
R
VR
24
9. Connect and measure the voltage across
the battery and then the resistor. Record
the values.
VB
VB = _______
R
VR
VR = _______
25
Conclusion(s)?
VB
R
VR
How do VB and VR compare?
26
10. Calculate:
VR1
VR 2
 __________
 __________
R1
R2
How do they compare?
They compares to ____________________
27
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.
28
D. Circuit Analysis
Two Resistors
Connected in Series
29
1. Measure the value of two resistors.
R1 = _________
R2 = _________
Then construct the following circuit.
30
2. Measure and record the current.
I = ____________
A
R1
R2
31
3. Measure and record the voltage across
the battery and both of the resistances.
A
I
R1
V1
R2
V2
VB
VB = _______ VR! = _______ VR2 = _______
32
4. How does VB compare to VR1 and VR2?
5. Calculate VR1/R1 and VR2/R2
______
______
What do these values compare to?
33
5. Calculate both VR1/R1 and VR2/R2.
VR1
VR 2
 __________
 __________
R1
R2
How do they compare?
What do these values compare to?
34
6. Write a conclusion about the current and
voltage in a circuit when two resistors are
connected in series with the battery.
IT  I R1  I R 2
VB  VR1  VR 2
35
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.
36
E. Circuit Analysis
Two Resistors
Connected in Parallel
38
1. Measure the value of both resistor.
R1 = _______
R2 = _______
Then construct the following circuit.
39
2. Record the value of the current
A
I
R1 R2
IT = ________
40
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.
A1 I1
A2 I2
R1 R2
41
Measure and record both currents.
A1 I1
A2 I2
R1 R2
IR1 = ____________
IR2 = ____________
42
4. How is the does the current through each
meter, IR1 and IR2 compare to the total
current IT?
IT = _______
IR1 = _______
IR2 = _______
A1 IR1
AR2IR2
R1 R2
43
5. Remove all ammeters which will give
you the following circuit.
R1 R2
44
6. Measure and record the voltage across
the battery VB, and the voltage across
the two resistors VR1 and VR2
VB
VR1
VB _______
VR1 _______
R1 R2
VR2
VR2 _______
45
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:
VB
V R1
VR 2
 ______
 ______
 ______
RT
RR1
RR 2
What do the values represent ?
How are they related ?
46
11. Write a conclusion about the current
and voltage in a circuit where 2
resistors are connected in parallel
with the battery.
IT  I R1  I R 2
VB  VR1  VR 2
47
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.
48
Final Summary
with some problems
49
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.
50
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.
51
Series Circuit
VT
R1
R2
R3
V1
V2
V3
Energy
VT  VConservati
V3
1  V2  on
V IR
IT  RT  I1  R1  I 2  R2  I 3  R3
Charg
I T  eI1Conservati
 I 2  I on
3
RT  R1  R2  R3
52
Resistance
in
Series
RT  R1  R2  R3
12 Ω, 25 Ω, and 42 Ω in series
The equivalent resistance is 79 Ω
53
Resistance in Series
Three 30-Ω light bulbs and
two 20-Ω heating elements
connected in series
The equivalent resistance is ….
130 ohms
54
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
55
Resistance in Series
Find the value of the unknown
resistance in the following:
a 20-Ω, a 18-Ω, and an unknown
resistor are connected in series to give
an equivalent resistance of 64-Ω
26 ohms
56
Parallel Circuit
R1
I1
IT
VT
R2
I2
R3
I3
V1
V2
V3
V
I
R
I T eIConservati
Charg
1  I 2  I 3 on
VT  VConservati
Energy
on
1  V2  V
3
VT V1
V3
V2



R2
RT R1
R3
1
1
1
1



RT R1
R2
R3
57
Resistance in Parallel
1
1
1
1
 

RT R1 R2 R3
Find the equivalent resistance when
a 4-Ω and an 8-Ω bulb are
connected in parallel.
2.7 ohm
58
Resistance in Parallel
Find the equivalent resistance
when a 16-Ω and an 8-Ω bulb are
connected in parallel.
5.3 ohm
59
Resistance in Parallel
Find the equivalent resistance
when a 20-Ω, a 10- Ω and a 5-Ω
bulb are connected in parallel.
2.9 ohm
60
Resistance in Parallel
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
61
Resistance in Parallel
Find the equivalent resistance of
two, three, four, and five 60-Ω bulb
are connected in parallel.
30 Ω 20 Ω 15 Ω 12 Ω
Is there a simple relationship for the
equivalent resistance of ‘n’ resistors
in parallel?
R/n
62
That’s all folks!
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