1. 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

2. 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

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

4. Finding Total or Equivalent Resistance

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

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

7. 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

8. 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?

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

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

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

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

13. 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

14. 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?

15. 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?

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

17. Checking Up on Ohms Law

18. Set up the following circuitA R
Measure and record the value of R

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

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

21. 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.

22. Remove Meter VB VR R

23. Measure and record: VB VR R
Voltage VB
Voltage VR

24. Conclusion(s) VB VR R
Voltage VB
Voltage VR

25. Resistances in Series

26. Set up the following circuitA R1 R2
Measure and record the values of R

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

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

29. 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.

30. Resistances in Parallel

31. Set up the following circuitA A1 A2 A2 R1 R2
Measure and record the values of R

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

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

34. 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.

35. 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.

36. 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.

37. Series Circuit R1 R2 R3 V1 V2 V3 VT

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

39. Resistance in Series
Three 30-Ω light bulbs and two 20-Ω heating elements connected in series
The equivalent resistance is ….
130 ohms

40. 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

41. 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

42. Parallel Circuit R1 I1 V1 R2 IT I2 V2 VT R3 I3 V3

43. Resistance in Parallel
Find the equivalent resistance when a 4-Ω and an 8-Ω bulb are connected in parallel.
2.7 ohm

44. Resistance in Parallel
Find the equivalent resistance when a 16-Ω and an 8-Ω bulb are connected in parallel.
5.3 ohm

45. 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

46. 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

47. 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

48. That’s all folks!