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Physics of Circuits. Created for BW Physics Middle School Science Teachers By Dick Heckathorn 23 April 2K + 8. Equipment. 1. Meter 2. Resistors 3. Battery 4. Connecting Wire. Table of Contents. 4 A. Finding Total or Equivalent Resistance of Resistors in Series

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physics of circuits

Physics of Circuits

Created for BW Physics

Middle School Science Teachers

By

Dick Heckathorn

23 April 2K + 8

equipment
Equipment
  • 1. Meter
  • 2. Resistors
  • 3. Battery
  • 4. Connecting Wire
table of contents
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
slide5

R1

R3

R2

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

_______ _______ _______

slide6

_______

_______

R1 + R2

R1 + R3

R2 + R

_______

  • 2. Connect two of the resistors end to end (in series) and measure the resistance across each pair.
slide7
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.
slide8

R1 + R2

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

R1 + R3

R2 + R3

slide9

R1 + R2 + R3

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

_____________

slide10
6. Does your rule for three resistors connected in series the same as for two resistors connected in series?
  • Yes ___ No ___
slide11
7. Your instructor hopes that you found the following to be true.

Remember this is for

ONLY resistors in series!

slide13

R3

R2

_________

_________

_________

R1

  • 1. Record the resistance of the three resistors that you measured before.
slide14

R1 : R2

R2 : R3

_________

_________

_________

R1 : R3

  • 2. Connect two of the resistors as shown (in parallel) and measure the resistance across each end.
slide15
3. Develop a rule from which can predict the equivalent resistance of two resistors in parallel?
slide16

R1 : R2 : R3

____________

  • 4. Connect all three resistors as shown, then measure the resistance across all three.
slide17
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 ___
slide18
6. The rule is:

Remember this is ONLY for

resistors in parallel!

slide20

A

R

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

measure and record

A

VA

VR

VB

Measure and record:

I

R

Voltage VA

Voltage VB

Current I

Voltage VR

conclusion s

A

VA

VR

VB

Conclusion(s)

I

R

I?

VB,I,andR?

VB,I,andR?

Compare VBwithVA and VR and

Compare VBwithVA and VR and

slide23
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.

slide25

VR

VB

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

R

VR = _______

VB = _______

conclusion s26

VR

VB

Conclusion(s)?

R

How do VB and VR compare?

10 calculate
10. Calculate:

How do they compare?

slide28
11. What does your instructor say about this?
  • Your instructor says that VBand VRshould be the same as the energy per charge given to the electrons by the battery VB and then removed by the resistor VR.
slide30

1. Measure the value of two resistors.

R1 = _________ R2 = _________

Then construct the following circuit.

slide31

A

R1

R2

2. Measure and record the current.

I = ____________

3 measure and record the voltage across the battery and both of the resistances

A

I

R1

VB

V1

V2

R2

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

VR2 = _______

VR! = _______

VB = _______

slide33
4. How does VB compare to VR1 and VR2?
  • 5. Calculate VR1/R1 and VR2/R2
  • ______ ______
  • What do these values compare to?
slide34

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

How do they compare?

What do these values compare to?

slide35
6. Write a conclusion about the current and voltage in a circuit when two resistors are connected in series with the battery.
slide36

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.

slide38

1. Measure the value of both resistor. R1 = _______ R2 = _______

Then construct the following circuit.

slide39

A

I

R2

R1

2. Record the value of the current

IT= ________

slide40

A1

I2

I1

A2

R2

R1

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.

slide41

A1

I2

I1

A2

R2

R1

Measure and record both currents.

IR1 = ____________ IR2 = ____________

slide42

A1

IR2

IR1

AR2

R2

R1

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

IT = _______IR1 = _______ IR2 = _______

slide43

R2

R1

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

slide44

VB

VR2

VR1

R2

R1

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

VB_______ VR1_______ VR2_______

slide45
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:
slide46

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

summary
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.
summary49
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.

summary50
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.

series circuit
Series Circuit

R3

R2

R1

V1

V3

V2

VT

resistance in series
ResistanceinSeries

12 Ω, 25 Ω, and 42 Ω in series

79 Ω

The equivalent resistance is

resistance in series53
Resistance in Series

Three 30-Ω light bulbs and two 20-Ω heating elements connected in series

The equivalent resistance is ….

130 ohms

resistance in series54
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

resistance in series55
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

parallel circuit
Parallel Circuit

R1

I1

V1

R2

I2

IT

V2

VT

R3

I3

V3

resistance in parallel
Resistance in Parallel

Find the equivalent resistance when a 4-Ω and an 8-Ω bulb are connected in parallel.

2.7 ohm

resistance in parallel58
Resistance in Parallel

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

5.3 ohm

resistance in parallel59
Resistance in Parallel

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

2.9 ohm

resistance in parallel60
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

resistance in parallel61
Resistance in Parallel

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

30 Ω

12 Ω

15 Ω

20 Ω

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

R/n

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