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### Physics of Circuits

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

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
- 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

_______

R1 + R2

R1 + R3

R2 + R

_______

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

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.

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

R1 + R3

R2 + R3

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

_____________

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

- Yes ___ No ___

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

Remember this is for

ONLY resistors in series!

R2

_________

_________

_________

R1

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

R2 : R3

_________

_________

_________

R1 : R3

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

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

____________

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

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 ___

R

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

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.

VB

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

R

VR = _______

VB = _______

10. Calculate:

How do they compare?

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.

1. Measure the value of two resistors.

R1 = _________ R2 = _________

Then construct the following circuit.

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 VB compare to VR1 and VR2?

- 5. Calculate VR1/R1 and VR2/R2
- ______ ______
- What do these values compare to?

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

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.

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

Then construct the following circuit.

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.

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 = _______

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 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

- 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.

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.

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.

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 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 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

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 Parallel

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

5.3 ohm

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 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 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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