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Understanding Ohm's Law and Series Resistors in Basic Electricity

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This extra credit lecture, led by Instructor Gary C. Meyer, provides an insightful review of Ohm's Law and power formulas critical for understanding basic electricity. Attendees will learn essential equations such as E = IR, I = E/R, and R(Total) for series resistors, alongside practical examples, including a case with resistors R1 (15 Ω), R2 (10 Ω), and R3 (5 Ω). This session aims to solidify foundational electrical concepts for students pursuing knowledge in electricity.

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Understanding Ohm's Law and Series Resistors in Basic Electricity

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  1. CST1511Basic 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: R1 = 15Ω R2 = 10Ω R3 = 5Ω R (Total) = _______
  4. Series Resistors R(Total) = R1 +R2 + R3 Example: R1 = 15Ω R2 = 10Ω R3 = 5Ω R (Total) = _ 30 ohms __
  5. Series Resistors R(Total) = R1 +R2 + R3 Example: R1 = 15Ω R2 = 10Ω R3 = 5Ω + 30 V - I (Total) =
  6. Series Resistors R(Total) = R1 +R2 + R3 Example: R1 = 15Ω R2 = 10Ω R3 = 5Ω + 30 V - I (Total) = E/R = 30/30 = 1 A
  7. Series Resistors R(Total) = R1 +R2 + R3 Example: R1 = 15Ω R2 = 10Ω R3 = 5Ω + 30 V - V (R2) = _____________
  8. Series Resistors R(Total) = R1 +R2 + R3 Example: R1 = 15Ω R2 = 10Ω R3 = 5Ω + 30 V - 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/(8000 + 2000) = 0.001 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/(1000 + 2000) = 0.0333 Amps R1 = 1k ohm R2 = 2k ohm V1 = I1 x R1 V2 = I2 x R2 E = 100 volts V1 = 0.0333 x 1000 = 33.3 v V2 = 0.0333 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 = .33 + .20 + 0.10 = 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 R2 = 500Ω R3 = 10Ω R (Total) = ______________
  21. Parallel Resistors 1/R(Total) = 1/R1 + 1/R2 + 1/R3 Problem R1 = 2 kΩ 1/R (total) = 1/2000 + 1/500 +1/10 1/R (Total)= .0005 + .002 + .1 1/R (Total) = .1025 R (Total) = 1/0.1025 R2 = 500Ω R3 = 10Ω R (Total) = 9.75 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) = 1.230 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) = 50 + 5 + 20 = 75 v V (R2) = 0.5 x 10 = 5 v V (R4) = 1 x 20 = 20 v
  33. Complete Worksheet 10Basic Electricity - 2 Optional – Extra Credit JPG FilePlace Worksheet in Dropbox for Worksheet 10
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