Created for CVCA Physics By Dick Heckathorn 3 March 2K + 5 Physics of Circuits Created for CVCA Physics By Dick Heckathorn 3 March 2K + 5

Table of Contents 4 Rules for combining resistors 18 My first circuit 25 Resistance in Series 30 Resistance in Parallel 38 Series Circuit Questions 41 Parallel Circuit Questions

Resistors Ohm’s Law Series and Parallel Circuits Created for CVCA Physics By Dick Heckathorn 1 April 2K + 4

Finding Total or Equivalent Resistance

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

2. Connect two of the resistors end to end (in series) and measure the resistance across any two. R1 + R2 R1 + R3 R2 + R3

3. Can you develop a rule from which you can predict the equivalent resistance of two resistors in series. R1 + R2 R1 + R3 R2 + R3

4. Connect all three resistors end to end (in series) and measure the resistance across all three. R1 + R2 + R3 5. Does your rule hold for three resistors connected in series?

6. Repeat the measurements using resistors, each with a different value. 7. Does your rule hold for three different resistors connected in series?

ONLY resistors in series! 8. Your instructor hopes that you found the following to be true. Remember this is for ONLY resistors in series!

1. Measure and record the resistance of three like resistors

2. Connect two of the resistors as shown (in parallel) and measure the resistance across each end. R1 : R2 R2 : R3 R1 : R3

3. Can you develop a rule from which can predict the equivalent resistance of two resistors in parallel? R2 R3 R1 : R2 R2 : R3 R1 : R3

4. Connect all three resistors as shown (in parallel) and measure the resistance across all three. R1 : R2 : R3 5. Does your rule hold for three resistors connected in parallel?

6. Repeat the measurements using resistors, each with a different value. 7. Does your rule hold for both two and three different resistors connected in parallel?

ONLY resistors in parallel.! 8. Your instructor hopes that you found the following to be true. Remember this is for ONLY resistors in parallel.!

Checking Up on Ohms Law

Set up the following circuit A R Measure and record the value of R

Measure and record: A I VB VR R Current I Voltage VB Voltage VR

Conclusion(s) A I VB VR R I? VR and VB? V, I, and R?

Is your value the same as the current? Be sure to keep track of units. Divide the voltage (V) by the resistance (R) . What did you get? Is your value the same as the current? Be sure to keep track of units.

Remove Meter VB VR R

Measure and record: VB VR R Voltage VB Voltage VR

Conclusion(s) VB VR R Voltage VB Voltage VR

Resistances in Series

Set up the following circuit A R1 R2 Measure and record the values of R

Measure and record: A I V1 R1 VB R2 V2 Current I Voltage VB Voltage V1 & V2

Conclusion(s) A V1 I R1 VB V2 R2 I? V1 , V2 and VB? V, I, and R?

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.

Resistances in Parallel

Set up the following circuit A A1 A2 A2 R1 R2 Measure and record the values of R

Measure and record: A I A1 I1 A2 I2 VB V1 V2 R1 R2 Current I2 Voltage VB Voltage V1 & V2

Conclusion(s) A I A1 I1 A2 I2 VB V1 V2 R1 R2 I? V1 , V2 and VB? V, I, and R?

Resistance Parallel 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.

Series Circuit R1 R2 R3 V1 V2 V3 VT

Resistance in Series 12 Ω, 25 Ω, and 42 Ω in series The equivalent resistance is 79 Ω

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

Find the value of the unknown resistance in the following: 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 R1 I1 V1 R2 IT I2 V2 VT R3 I3 V3

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- Ω and 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 20 Ω 15 Ω 12 Ω Is there a simple relationship for the equivalent resistance of ‘n’ resistors in parallel? R/n

That’s all folks!