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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

Created for BW Physics

Middle School Science Teachers

By

Dick Heckathorn

23 April 2K + 8

• 1. Meter

• 2. Resistors

• 3. Battery

• 4. Connecting Wire

• 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

### A. Finding Total or Equivalent Resistanceof resistors connectedinSeries

R1

R3

R2

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

_______ _______ _______

_______

R1 + R2

R1 + R3

R2 + R

_______

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

R replace the two resistors and has the same effect in a circuit as the two resistors. 1 + R2

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

R1 + R3

R2 + R3

R replace the two resistors and has the same effect in a circuit as the two resistors. 1 + R2 + R3

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

_____________

Remember this is for

ONLY resistors in series!

### B. Finding Total or Equivalent Resistance of Resistors in Parallel

R Parallel3

R2

_________

_________

_________

R1

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

R Parallel1 : R2

R2 : R3

_________

_________

_________

R1 : R3

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

R resistance of two resistors in parallel?1 : R2 : R3

____________

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

• 6. The rule is: three resistors connected in parallel the same for finding the equivalent resistance of two resistors connected in parallel?

Remember this is ONLY for

resistors in parallel!

### C. Circuit Analysis three resistors connected in parallel the same for finding the equivalent resistance of two resistors connected in parallel? One Resistor

A three resistors connected in parallel the same for finding the equivalent resistance of two resistors connected in parallel?

R

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

A three resistors connected in parallel the same for finding the equivalent resistance of two resistors connected in parallel?

VA

VR

VB

Measure and record:

I

R

Voltage VA

Voltage VB

Current I

Voltage VR

A three resistors connected in parallel the same for finding the equivalent resistance of two resistors connected in parallel?

VA

VR

VB

Conclusion(s)

I

R

I?

VB,I,andR?

VB,I,andR?

Compare VBwithVA and VR and

Compare VBwithVA and VR and

• 6. Divide the voltage ( three resistors connected in parallel the same for finding the equivalent resistance of two resistors connected in parallel?VB) by the resistance (R).

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

Be sure to keep track of units.

V three resistors connected in parallel the same for finding the equivalent resistance of two resistors connected in parallel?R

VB

8. Remove Ammeter

R

V three resistors connected in parallel the same for finding the equivalent resistance of two resistors connected in parallel?R

VB

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

R

VR = _______

VB = _______

V three resistors connected in parallel the same for finding the equivalent resistance of two resistors connected in parallel?R

VB

Conclusion(s)?

R

How do VB and VR compare?

10. Calculate: three resistors connected in parallel the same for finding the equivalent resistance of two resistors connected in parallel?

How do they compare?

• 11. What does your instructor say about this? three resistors connected in parallel the same for finding the equivalent resistance of two resistors connected in parallel?

• 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.

### D. Circuit Analysis three resistors connected in parallel the same for finding the equivalent resistance of two resistors connected in parallel?Two ResistorsConnected in Series

1. Measure the value of two resistors. three resistors connected in parallel the same for finding the equivalent resistance of two resistors connected in parallel?

R1 = _________ R2 = _________

Then construct the following circuit.

A three resistors connected in parallel the same for finding the equivalent resistance of two resistors connected in parallel?

R1

R2

2. Measure and record the current.

I = ____________

A three resistors connected in parallel the same for finding the equivalent resistance of two resistors connected in parallel?

I

R1

VB

V1

V2

R2

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

VR2 = _______

VR! = _______

VB = _______

• 4. How does V three resistors connected in parallel the same for finding the equivalent resistance of two resistors connected in parallel?B compare to VR1 and VR2?

• 5. Calculate VR1/R1 and VR2/R2

• ______ ______

• What do these values compare to?

5. Calculate both V three resistors connected in parallel the same for finding the equivalent resistance of two resistors connected in parallel?R1/R1 and VR2/R2.

How do they compare?

What do these values compare to?

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.

### E. Circuit Analysis circuit when two resistors are connected in series with the battery.Two ResistorsConnected in Parallel

1. Measure the value of both resistor. circuit when two resistors are connected in series with the battery.R1 = _______ R2 = _______

Then construct the following circuit.

A circuit when two resistors are connected in series with the battery.

I

R2

R1

2. Record the value of the current

IT= ________

A circuit when two resistors are connected in series with the battery.1

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.

A circuit when two resistors are connected in series with the battery.1

I2

I1

A2

R2

R1

Measure and record both currents.

IR1 = ____________ IR2 = ____________

A circuit when two resistors are connected in series with the battery.1

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 = _______

R circuit when two resistors are connected in series with the battery.2

R1

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

V circuit when two resistors are connected in series with the battery.B

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_______

• 7. How is the voltage of the battery circuit when two resistors are connected in series with the battery.VB related to the voltage through each resistor VR1 and VR2?

• VB_______ VR1_______ VR2_______

• Calculate the following:

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

Summary circuit where 2 resistors are connected in parallel with the battery.

• 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.

### Final Summary circuit where 2 resistors are connected in parallel with the battery.with some problems

Summary circuit where 2 resistors are connected in parallel with the battery.

• 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.

Summary circuit where 2 resistors are connected in parallel with the battery.

• 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 circuit where 2 resistors are connected in parallel with the battery.

R3

R2

R1

V1

V3

V2

VT

Resistance circuit where 2 resistors are connected in parallel with the battery.inSeries

12 Ω, 25 Ω, and 42 Ω in series

79 Ω

The equivalent resistance is

Resistance in Series circuit where 2 resistors are connected in parallel with the battery.

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

The equivalent resistance is ….

130 ohms

Resistance in Series circuit where 2 resistors are connected in parallel with the battery.

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 Series circuit where 2 resistors are connected in parallel with the battery.

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 circuit where 2 resistors are connected in parallel with the battery.

R1

I1

V1

R2

I2

IT

V2

VT

R3

I3

V3

Resistance in Parallel circuit where 2 resistors are connected in parallel with the battery.

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

2.7 ohm

Resistance in Parallel circuit where 2 resistors are connected in parallel with the battery.

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

5.3 ohm

Resistance in Parallel circuit where 2 resistors are connected in parallel with the battery.

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

2.9 ohm

Resistance in Parallel circuit where 2 resistors are connected in parallel with the battery.

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 circuit where 2 resistors are connected in parallel with the battery.

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