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Extra Credit Lecture Gary C. Meyer, Instructor Review of Ohms Law/Power Formulas E = IR I = E/R R = E/I P = EI P = I2R P = E2/R Series Resistors R(Total) = R1 +R2 + R3 Example: R1 = 15Ω R2 = 10Ω R (Total) = _______ R3 = 5Ω Series Resistors R(Total) = R1 +R2 + R3 Example: R1 = 15Ω R2 = 10Ω R (Total) = R3 = 5Ω _ 30 ohms __ Series Resistors R(Total) = R1 +R2 + R3 Example: R1 = 15Ω R2 = 10Ω + 30 V I (Total) = R3 = 5Ω Series Resistors R(Total) = R1 +R2 + R3 Example: R1 = 15Ω R2 = 10Ω R3 = 5Ω + 30 V I (Total) = E/R = 30/30 = 1 A Series Resistors R(Total) = R1 +R2 + R3 Example: R1 = 15Ω R2 = 10Ω + 30 V V (R2) = _____________ R3 = 5Ω 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 Current in Series Circuit Use Ohm’s Law Example: R1 = 8k ohm R2 = 2k ohm I (R1) = ? E = 10 volts I(R1) = 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 Voltage in Series Circuit Voltage Divides Across Resistors Example: First Find Current. Next find voltages. I= R1 = 1k ohm V1 = I1 x R1 R2 = 2k ohm V2 = I2 x R2 E = 100 volts V1 = V2 = 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 Parallel Resistors (For Two) R(Total) = (R1 x R2)/(R1 + R2) Example: Rt = ? R1 = 100 R2 = 50 R (Total) = 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 Parallel Resistors (For Two) R(Total) = (R1 x R2)/(R1 + R2) Example: Rt = ? R1 = 2 kohms R2 = 3 kohms R (Total) = ? 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 Current In Parallel Circuit Use Ohm’s Law Example: I1 = E/R1 = 100/25 = 4 A I2= E/R2 = 100/50 = 2 A R1 = 25 R2 = 50 E = 100 v It = I1 + I2 = 6 Amps Power In Parallel Circuit Use Power Formulas Example: P1 = E x I = 100 x 4 = 400 watts P2= E x I = 100 x 2 = 200 watts R1 = 25 R2 = 50 E = 100 v Pt = P1 + P2 = 600 watts 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 Parallel Resistors 1/R(Total) = 1/R1 + 1/R2 + 1/R3 Problem R1 = 2 kΩ R2 = 500Ω R3 = 10Ω R (Total) = ______________ 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 R2 = 500Ω 1/R (Total) = .1025 R (Total) = 1/0.1025 R3 = 10Ω R (Total) = 9.75 ohms Parallel Resistors 1/R(Total) = 1/R1 + 1/R2 + 1/R3 Problem I = E/R Solve for all currents. R1 = 2 kΩ I (R1) = I (R2) = R2 = 500Ω I (R3) = I (total) = R3 = 10Ω 12 v Parallel Resistors 1/R(Total) = 1/R1 + 1/R2 + 1/R3 Problem I = E/R Solve for all currents. R1 = 2 kΩ R2 = 500Ω I (R1) = 12/2000 = .006 A I (R2) = 12/500 = .024 A I (R3) = 12 /10 = 1.2 A R3 = 10Ω I (total) = 1.230 A 12 v Series/Parallel Resistors Use Same Principles Example: R2 = 50 R1 = 100 R4 = 60 R3 = 50 R (Total) = 100 + (50x50)/(50+50) + 60 = 185Ω 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 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 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 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 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 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) = 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 (R2) = V (R4) = V (Total) = 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 (R2) = 0.5 x 10 = 5 v V (R4) = 1 x 20 = 20 v V (Total) = 50 + 5 + 20 = 75 v Optional – Extra Credit JPG File Place Worksheet in Dropbox for Worksheet 10