1. CST1511 Basic Electricity - 2
Extra Credit Lecture
Gary C. Meyer, Instructor

2. Review of Ohms Law/Power Formulas
E = IR
I = E/R
R = E/I
P = EI
P = I2R
P = E2/R

3. Series Resistors R(Total) = R1 +R2 + R3 Example: _______

4. Series Resistors R(Total) = R1 +R2 + R3 Example: _ 30 ohms __

5. Series Resistors + 30 V - R(Total) = R1 +R2 + R3 Example: I (Total) =

6. Series Resistors + 30 V - R(Total) = R1 +R2 + R3 Example:
I (Total) = E/R = 30/30 = 1 A

7. Series Resistors + 30 V - R(Total) = R1 +R2 + R3 Example:

8. Series Resistors + 30 V - R(Total) = R1 +R2 + R3 Example:
V (R2) = I x R = 1 x 10 = 10 v

9. Current in Series Circuit
Use Ohm’s Law
Example:
R1 = 8k ohm
R2 = 2k ohm
I (R1) = ?
E = 10 volts
I(R1) =

10. Current in Series Circuit
Use Ohm’s Law
Example:
R1 = 8k ohm
R2 = 2k ohm
I R1 = ?
E = 10 volts
IR1 =
10/( ) = Amps

11. Voltage in Series Circuit
Voltage Divides Across Resistors
Example: First Find Current. Next find voltages.
I =
R1 = 1k ohm
R2 = 2k ohm
V1 = I1 x R1
V2 = I2 x R2
E = 100 volts
V1 =
V2 =

12. Voltage in Series Circuit
Voltage Divides Across Resistors
Example: First Find Current. Next find voltages.
I =
100/( ) = Amps
R1 = 1k ohm
R2 = 2k ohm
V1 = I1 x R1
V2 = I2 x R2
E = 100 volts
V1 =
x 1000 = 33.3 v
V2 =
x 2000 = 66.6 v

13. Parallel Resistors (For Two)
R(Total) = (R1 x R2)/(R1 + R2)
Example: Rt = ?
R1 = 100
R2 = 50
R (Total) =

14. Parallel Resistors (For Two)
R(Total) = (R1 x R2)/(R1 + R2)
Example: Rt = ?
R1 = 100
R2 = 50
R (Total) =
(100 x 50)/150 = 33.33Ω

15. Parallel Resistors (For Two)
R(Total) = (R1 x R2)/(R1 + R2)
Example: Rt = ?
R1 = 2 kohms
R2 = 3 kohms
R (Total) = ?

16. Parallel Resistors (For Two)
R(Total) = (R1 x R2)/(R1 + R2)
Example: Rt = ?
R1 = 2 kohms
R2 = 3 kohms
R (Total) =
(2000 x 3000)/5000 = 1200 Ω

17. Current In Parallel Circuit
Use Ohm’s Law
Example: I1 = I2=
E/R1 = 100/25 = 4 A
E/R2 = 100/50 = 2 A
R1 = 25
R2 = 50
E = 100 v
It =
I1 + I2 = 6 Amps

18. Power In Parallel Circuit
Use Power Formulas
Example: P1 = P2=
E x I = 100 x 4 = 400 watts
E x I = 100 x 2 = 200 watts
R1 = 25
R2 = 50
E = 100 v
Pt =
P1 + P2 = 600 watts

19. Parallel Resistors 1/R(Total) = 1/R1 + 1/R2 + 1/R3
Example: 1/Rt = 1/3 + 1/5 + 1/10 = = 0.63 Ω
R1 = 3Ω
R2 = 5Ω
R3 = 10Ω
R (Total) = 1/0.63 = 1.59 ohms

20. Parallel Resistors 1/R(Total) = 1/R1 + 1/R2 + 1/R3 Problem R1 = 2 kΩ

21. Parallel Resistors 1/R(Total) = 1/R1 + 1/R2 + 1/R3 Problem R1 = 2 kΩ
R (Total) = ohms

22. Parallel Resistors 1/R(Total) = 1/R1 + 1/R2 + 1/R3 Problem I = E/R
Solve for all currents.
I (R1) =
I (R2) =
I (R3) =
I (total) =
R1 = 2 kΩ
R2 = 500Ω
R3 = 10Ω
12 v

23. Parallel Resistors 1/R(Total) = 1/R1 + 1/R2 + 1/R3 Problem I = E/R
Solve for all currents.
I (R1) = 12/2000 = .006 A
I (R2) = 12/500 = .024 A
I (R3) = 12 /10 = 1.2 A
I (total) = A
R1 = 2 kΩ
R2 = 500Ω
R3 = 10Ω
12 v

24. Series/Parallel Resistors
Use Same Principles
Example:
R2 = 50
R1 = 100
R4 = 60
R3 = 50
R (Total) =
100 + (50x50)/(50+50) + 60 = 185Ω

25. Currents in Combined Circuit
Use Resistance Rules + Ohm’s Law
Example: Rt = 185 ohms from a previous example.
R2 = 50
R1 = 100
R4 = 60
R3 = 50
Equal resistors = Equal currents
E = 370 v
I (Total) =
E/R = 370/185 = 2 A
IR2 = ? IR3 =?
IR2 = IR3 = 1 A

26. Voltages in Combined Circuit
Use Resistance Rules + Ohm’s Law
Example: Rt = 185 ohms from previous example.
R2 = 50
R1 = 100
R4 = 60
R3 = 50
E = 370 v
I (Total) =
E/R = 370/185 = 2 A
VR1 =
IR1 x R1 = 2 x 100 = 200 v

27. Voltages in Combined Circuit
Use Resistance Rules + Ohm’s Law
Example: Rt = 185 ohms from previous example.
R2 = 50
R1 = 100
R4 = 60
R3 = 50
E = 370 v
I (Total) =
E/R = 370/185 = 2 A
VR2 =
IR2 x R2 = 1 x 50 = 50 v

28. Voltages in Combined Circuit
Use Resistance Rules + Ohm’s Law
Example: Rt = 185 ohms from previous example.
R2 = 50
R1 = 100
R4 = 60
R3 = 50
E = 370 v
I (Total) =
E/R = 370/185 = 2 A
VR4 =
IR3 x R3 = 2 x 60 = 120 v

29. Parallel Resistor Currents
Example Problem
Example: What is the current in the 20 ohm resistor?
R2 =20
R1 = 100
R4 = 100
IR2
R3 = 40
It = 0.6 A
IR3
IR2 = R3/(R2 + R3) x (It) = 40/60 x .6 = 0.4 A
IR3 = R2/(R2 + R3) x (It) = 20/60 x .6 = 0.2 A

30. Parallel Resistor Currents
Problem
Example: What is the current in the 20 ohm resistor?
R2 =10
R1 = 50
R4 = 20
IR2
R3 = 10
It = 1.0 A
IR3
IR2 = R3/(R2 + R3) x (It) =
IR3 = R2/(R2 + R3) x (It) =

31. Parallel/Series Resistor Voltages
Problem
Example: What is the current in the 20 ohm resistor?
R2 =10
R1 = 50
R4 = 20
IR2
R3 = 10
It = 1.0 A
IR3
V (R1) =
V (Total) =
V (R2) =
V (R4) =

32. Parallel/Series Resistor Voltages
Solution
Example: What is the current in the 20 ohm resistor?
R2 =10
R1 = 50
R4 = 20
IR2
R3 = 10
It = 1.0 A
IR3
V (R1) = 1 x 50 = 50v
V (Total) = = 75 v
V (R2) = 0.5 x 10 = 5 v
V (R4) = 1 x 20 = 20 v

33. Complete Worksheet 10 Basic Electricity - 2
Optional – Extra Credit
JPG File Place Worksheet in Dropbox for Worksheet 10