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Extra Credit Lecture Gary C. Meyer, Instructor

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

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Series Resistors R(Total) = R1 +R2 + R3 Example: R1 = 15Ω R2 = 10Ω R3 = 5Ω R (Total) = _______

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Series Resistors R(Total) = R1 +R2 + R3 Example: R1 = 15Ω R2 = 10Ω R3 = 5Ω R (Total) = _ 30 ohms __

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Series Resistors R(Total) = R1 +R2 + R3 Example: R1 = 15Ω R2 = 10Ω R3 = 5Ω I (Total) = + 30 V -

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Series Resistors R(Total) = R1 +R2 + R3 Example: R1 = 15Ω R2 = 10Ω R3 = 5Ω I (Total) = E/R = 30/30 = 1 A + 30 V -

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Series Resistors R(Total) = R1 +R2 + R3 Example: R1 = 15Ω R2 = 10Ω R3 = 5Ω V (R2) = _____________ + 30 V -

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Series Resistors R(Total) = R1 +R2 + R3 Example: R1 = 15Ω R2 = 10Ω R3 = 5Ω V (R2) = I x R = 1 x 10 = 10 v + 30 V -

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

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Current in Series Circuit Use Ohm’s Law Example: R1 = 8k ohm IR1 =10/( 8 000 + 2000) = 0.001 Amps R2 = 2k ohm E = 10 volts I R1 = ?

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Voltage in Series Circuit Voltage Divides Across Resistors Example: First Find Current. Next find voltages. R1 = 1k ohm I = R2 = 2k ohm E = 100 volts V1 = I1 x R1V2 = I2 x R2 V1 =V2 =

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Voltage in Series Circuit Voltage Divides Across Resistors Example: First Find Current. Next find voltages. R1 = 1k ohm I = 100/(1000 + 2000) = 0.0333 Amps R2 = 2k ohm E = 100 volts V1 = I1 x R1V2 = I2 x R2 V1 =0.0333 x 1000 = 33.3 vV2 =0.0333 x 2000 = 66.6 v

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

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

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

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

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

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

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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 R (Total) = 1/0.63 = 1.59 ohms R2 = 5Ω R3 = 10Ω

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Parallel Resistors 1/R(Total) = 1/R1 + 1/R2 + 1/R3 Problem R1 = 2 kΩ R (Total) = ______________ R2 = 500Ω R3 = 10Ω

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Parallel Resistors 1/R(Total) = 1/R1 + 1/R2 + 1/R3 Problem R1 = 2 kΩ R (Total) = 9.75 ohms R2 = 500Ω R3 = 10Ω 1/R (total) = 1/2000 + 1/500 +1/10 1/R (Total)=.0005 +.002 +.1 1/R (Total) =.1025 R (Total) = 1/0.1025

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

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Parallel Resistors 1/R(Total) = 1/R1 + 1/R2 + 1/R3 Problem I = E/R R1 = 2 kΩ R2 = 500Ω R3 = 10Ω 12 v 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

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

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

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

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

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

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Parallel Resistor Currents Example Problem Example: What is the current in the 20 ohm resistor? R1 = 100 R2 =20 R3 = 40 R4 = 100 It = 0.6 A 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 IR2 IR3

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

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

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

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Optional – Extra Credit JPG File Place Worksheet in Dropbox for Worksheet 10

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