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Resistance, Ohm’s Law & Circuits Physics 1161: Lecture 08 Homework, keep lots of digits! Georg Ohm

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Last Time Capacitors C = Q/V -- definition – PhysicalC = 0 A/d – Series 1/C eq = 1/C 1 + 1/C 2 – ParallelC eq = C 1 + C 2 – EnergyU = 1/2 QV Resistors R = V/ I –Physical R = L/A –Series R eq = R 1 + R 2 –Parallel1/R eq = 1/R 1 + 1/R 2 –Power P = IV Today

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Preflight 8.1 Two cylindrical resistors are made from the same material. They are of equal length but one has twice the diameter of the other. 1.R 1 > R 2 2.R 1 = R 2 3.R 1 < R 2 21

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Practice… – Calculate I when =24 Volts and R = 8 – Ohm’s Law: V =IR Simple Circuit R I I I = V/R = 3 Amps

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Preflight 8.3 Compare I 1 the current through R 1, with I 10 the current through R 10. 1.I 1 < I 10 2.I 1 = I 10 3.I 1 > I 10 R 1 =1 00 R 10 =10 Note: I is the same everywhere in this circuit!

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Compare V 1 the voltage across R 1, with V 10 the voltage across R 10. R 1 =1 00 R 10 =10 1.V 1 >V 10 2.V 1 =V 10 3.V 1 < V 10

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Compare V 1 the voltage across R 1, with V 10 the voltage across R 10. R 1 =1 00 R 10 =10 V 1 = I 1 R 1 = 1 x I V 10 = I 10 R 10 = 10 x I 1.V 1 >V 10 2.V 1 =V 10 3.V 1 < V 10

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Practice: Resistors in Series Calculate the voltage across each resistor if the battery has potential V 0 = 22 volts. R 12 = R 1 + R 2 V 12 = V 1 + V 2 I 12 = I 1 = I 2 = 11 R 12 00 = V 0 = 22 Volts = V 12 /R 12 = 2 Amps Expand: V 1 = I 1 R 1 V 2 = I 2 R 2 = 2 x 1 = 2 Volts = 2 x 10 = 20 Volts R 1 =1 00 R 2 =10 Check: V 1 + V 2 = V 12 ? Simplify (R 1 and R 2 in series): R 1 =1 00 R 2 =10 YES!

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Preflight 8.5 What happens to the current through R 2 when the switch is closed? Increases Remains Same Decreases V 2 = ε = I 2 R 2

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What happens to the current through the battery when the switch is closed? 1.Increases 2.Remains Same 3.Decreases

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What happens to the current through the battery when the switch is closed? 1.Increases 2.Remains Same 3.Decreases

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Practice: Resistors in Parallel Determine the current through the battery. Let E = 60 Volts, R 2 = 20 and R 3 =30 . 1/R 23 = 1/R 2 + 1/R 3 V 23 = V 2 = V 3 I 23 = I 2 + I 3 R2R2 R3R3 R 23 Simplify: R 2 and R 3 are in parallel R 23 = 12 = 60 Volts = V 23 /R 23 = 5 Amps

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Why is it dangerous to use one power strip to plug in and use simultaneously your microwave, coffee pot, toaster, and hair dryer (current through hair dryer is 10 A)? 1.The resistance of the kitchen circuit is too high. 2.The voltage across the kitchen circuit is too high. 3.The current in the kitchen circuit is too high.

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Why is it dangerous to use one power strip to plug in and use simultaneously your microwave, coffee pot, toaster, and hair dryer (current through hair dryer is 10 A)? 1.The resistance of the kitchen circuit is too high. 2.The voltage across the kitchen circuit is too high. 3.The current in the kitchen circuit is too high.

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Preflight 8.6, 8.7 Which configuration has the smallest resistance? 1 2 3 123 Which configuration has the largest resistance? 2 R 2R R/2

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Parallel + Series Tests Resistors R 1 and R 2 are in series if and only if every loop that contains R 1 also contains R 2 Resistors R 1 and R 2 are in parallel if and only if you can make a loop that has ONLY R 1 and R 2 Same rules apply to capacitors!!

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Voltage Current Resistance Series Parallel Summary Different for each resistor. V total = V 1 + V 2 Increases R eq = R 1 + R 2 Same for each resistor I total = I 1 = I 2 Same for each resistor. V total = V 1 = V 2 Decreases 1/R eq = 1/R 1 + 1/R 2 Wiring Each resistor on the same wire. Each resistor on a different wire. Different for each resistor I total = I 1 + I 2 R1R1 R2R2 R1R1 R2R2

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