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• Resistance Demo 1055 Ramp with balls as resistor (Ohm’s Law)—change height Ohm’s Law Demo 1228 Water resistance, effect of A, L on flow
• Demo 1091: lots of appliances to blow fuse—do this while ACT is going on
• ### Lect05 handout

1. 1. Circuits and Ohm’s Law Physics 102: Lecture 05
2. 2. Summary of Last Time <ul><li>Capacitors </li></ul><ul><ul><li>Physical C =  0 A/d C=Q/V </li></ul></ul><ul><ul><li>Series 1/C eq = 1/C 1 + 1/C 2 </li></ul></ul><ul><ul><li>Parallel C eq = C 1 + C 2 </li></ul></ul><ul><ul><li>Energy U = 1/2 QV </li></ul></ul><ul><li>Resistors </li></ul><ul><ul><li>Physical R =  L/A V=IR </li></ul></ul><ul><ul><li>Series R eq = R 1 + R 2 </li></ul></ul><ul><ul><li>Parallel 1/R eq = 1/R 1 + 1/R 2 </li></ul></ul><ul><ul><li>Power P = IV </li></ul></ul>Summary of Today
3. 3. Electric Terminology <ul><li>Current: Moving Charges </li></ul><ul><ul><li>Symbol: I </li></ul></ul><ul><ul><li>Unit: Amp  Coulomb/second </li></ul></ul><ul><ul><li>Count number of charges which pass point/sec </li></ul></ul><ul><ul><li>Direction of current is direction that + flows </li></ul></ul><ul><li>Power: Energy/Time </li></ul><ul><ul><li>Symbol: P </li></ul></ul><ul><ul><li>Unit: Watt  Joule/second = Volt Coulomb/sec </li></ul></ul><ul><ul><li>P = VI </li></ul></ul>
4. 4. Physical Resistor <ul><li>Resistance: Traveling through a resistor, electrons bump into things which slows them down. </li></ul><ul><li>R =  L /A </li></ul><ul><ul><li> : Resistivity: Density of bumps </li></ul></ul><ul><ul><li>L : Length of resistor </li></ul></ul><ul><ul><li>A : Cross sectional area of resistor </li></ul></ul><ul><li>Ohms Law I = V/R </li></ul><ul><ul><li>Cause and effect (sort of like a=F/m) </li></ul></ul><ul><ul><ul><li>potential difference cause current to flow </li></ul></ul></ul><ul><ul><ul><li>resistance regulate the amount of flow </li></ul></ul></ul><ul><ul><li>Double potential difference  double current </li></ul></ul><ul><ul><li>I = (VA)/ (  L) </li></ul></ul>A L
5. 5. Preflight 5.1 <ul><li>Two cylindrical resistors are made from the same material. They are of equal length but one has twice the diameter of the other. </li></ul><ul><li>R 1 > R 2 </li></ul><ul><li>R 1 = R 2 </li></ul><ul><li>R 1 < R 2 </li></ul>2 1
6. 6. Comparison: Capacitors vs. Resistors <ul><li>Capacitors store energy as separated charge: U=QV/2 </li></ul><ul><ul><li>Capacitance: ability to store separated charge: C =  0 A/d </li></ul></ul><ul><ul><li>Voltage drop determines charge : V=Q/C </li></ul></ul><ul><li>Resistors dissipate energy as power: P=VI </li></ul><ul><ul><li>Resistance: how difficult it is for charges to get through: R =  L /A </li></ul></ul><ul><ul><li>Voltage drop determines current : V=IR </li></ul></ul><ul><li>Don’t mix capacitor and resistor equations! </li></ul>
7. 7. <ul><li>Visualization </li></ul><ul><li>Practice… </li></ul><ul><ul><li>Calculate I when  =24 Volts and R = 8  </li></ul></ul><ul><ul><li>Ohm’s Law: V =IR </li></ul></ul>Simple Circuit R  I I Example I = V/R = 3 Amps
8. 8. Resistors in Series <ul><li>One wire: </li></ul><ul><ul><li>Effectively adding lengths: </li></ul></ul><ul><ul><ul><li>R eq =  (L 1 +L 2 )/A </li></ul></ul></ul><ul><ul><li>Since R  L add resistance: </li></ul></ul>R eq = R 1 + R 2 R R = 2R
9. 9. Resistors in Series: “Proof” that R eq =R 1 +R 2 <ul><li>Resistors connected end-to-end: </li></ul><ul><ul><li>If charge goes through one resistor, it must go through other. </li></ul></ul><ul><li>I 1 = I 2 = I eq </li></ul><ul><ul><li>Both have voltage drops: </li></ul></ul><ul><li>V 1 + V 2 = V eq </li></ul>R 1 R 2 R eq R eq = V eq = V 1 + V 2 = R 1 + R 2 I eq I eq
10. 10. Preflight 5.3 <ul><li>Compare I 1 the current through R 1 , with I 10 the current through R 10 . </li></ul><ul><li>I 1 <I 10 </li></ul><ul><li>I 1 =I 10 </li></ul><ul><li>I 1 >I 10 </li></ul>R 1 =1   0 R 10 =10 
11. 11. Compare V 1 the voltage across R 1 , with V 10 the voltage across R 10 . 1. V 1 >V 10 2. V 1 =V 10 3. V 1 <V 10 ACT: Series Circuit R 1 =1   0 R 10 =10 
12. 12. Practice: Resistors in Series <ul><li>Calculate the voltage across each resistor if the battery has potential ε 0 = 22 volts. </li></ul><ul><ul><li>R 12 = R 1 + R 2 </li></ul></ul><ul><ul><li>V 12 = V 1 + V 2 </li></ul></ul><ul><ul><li>I 12 = I 1 = I 2 </li></ul></ul>= 11  = ε 0 = 22 Volts = V 12 /R 12 = 2 Amps <ul><li>Expand: </li></ul><ul><ul><li>V 1 = I 1 R 1 </li></ul></ul><ul><ul><li>V 2 = I 2 R 2 </li></ul></ul>= 2 x 1 = 2 Volts = 2 x 10 = 20 Volts Check: V 1 + V 2 = V 12 ? Simplify (R 1 and R 2 in series): Example R 12  0 R 1 =1   0 R 2 =10  R 1 =1   0 R 2 =10 
13. 13. Resistors in Parallel <ul><li>Two wires: </li></ul><ul><ul><li>Effectively adding the Area </li></ul></ul><ul><ul><li>Since R  1/A add 1/R: </li></ul></ul>R R = R/2 1/R eq = 1/R 1 + 1/R 2
14. 14. Resistors in Parallel <ul><li>Both ends of resistor are connected: </li></ul><ul><ul><li>Current is split between two wires: </li></ul></ul><ul><li>I 1 + I 2 = I eq </li></ul><ul><ul><li>Voltage is same across each: </li></ul></ul><ul><li>V 1 = V 2 = V eq </li></ul>R eq R 2 R 1
15. 15. Preflight 5.5 <ul><li>What happens to the current through R 2 when the switch is closed? </li></ul><ul><li>Increases </li></ul><ul><li>Remains Same </li></ul><ul><li>Decreases </li></ul>What happens to the current through the battery? (1) Increases (2) Remains Same (3) Decreases ACT: Parallel Circuit
16. 16. Practice: Resistors in Parallel <ul><li>Determine the current through the battery. </li></ul><ul><li>Let ε = 60 Volts, R 2 = 20  and R 3 =30  . </li></ul><ul><ul><li>1/R 23 = 1/R 2 + 1/R 3 </li></ul></ul><ul><ul><li>V 23 = V 2 = V 3 </li></ul></ul><ul><ul><li>I 23 = I 2 + I 3 </li></ul></ul>R 23 = 12  = 60 Volts = V 23 /R 23 = 5 Amps Simplify: R 2 and R 3 are in parallel Example R 2 R 3  R 23 
17. 17. Johnny “Danger” Powells uses one power strip to plug in his microwave, coffee pot, space heater, toaster, and guitar amplifier all into one outlet. Toaster This is dangerous because… (By the way, power strips are wired in parallel.) ACT: Your Kitchen 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. Coffee Pot Microwave 10 A 5 A 10 A 25 A
18. 18. ACT/Preflight 5.6, 5.7 <ul><li>Which configuration has the smallest resistance? </li></ul><ul><li>1 </li></ul><ul><li>2 </li></ul><ul><li>3 </li></ul>1 2 3 Which configuration has the largest resistance?
19. 19. Try it! R 1 R 2 R 3 Calculate current through each resistor. R 1 = 10  , R 2 = 20  R 3 = 30    V <ul><li>Simplify: R 2 and R 3 are in parallel </li></ul><ul><ul><li>1/R 23 = 1/R 2 + 1/R 3 </li></ul></ul><ul><ul><li>V 23 = V 2 = V 3 </li></ul></ul><ul><ul><li>I 23 = I 2 + I 3 </li></ul></ul><ul><li>Simplify: R 1 and R 23 are in series </li></ul><ul><ul><li>R 123 = R 1 + R 23 </li></ul></ul><ul><ul><li>V 123 = V 1 + V 23 =  </li></ul></ul><ul><ul><li>I 123 = I 1 = I 23 = I battery </li></ul></ul>: R 23 = 12  : R 123 = 22  R 1  : I 123 = 44 V/22  A Power delivered by battery? P=IV = 2  44 = 88W Example R 123  R 23 
20. 20. Try it! (cont.) Calculate current through each resistor. R 1 = 10  , R 2 = 20  R 3 = 30    V <ul><li>Expand: R 2 and R 3 are in parallel </li></ul><ul><ul><li>1/R 23 = 1/R 2 + 1/R 3 </li></ul></ul><ul><ul><li>V 23 = V 2 = V 3 </li></ul></ul><ul><ul><li>I 23 = I 2 + I 3 </li></ul></ul><ul><li>Expand: R 1 and R 23 are in series </li></ul><ul><ul><li>R 123 = R 1 + R 23 </li></ul></ul><ul><ul><li>V 123 = V 1 + V 23 =  </li></ul></ul><ul><ul><li>I 123 = I 1 = I 23 = I battery </li></ul></ul> : I 23 = 2 A : V 23 = I 23 R 23 = 24 V I 2 = V 2 /R 2 =24/20=1.2A I 3 = V 3 /R 3 =24/30=0.8A Example R 1 R 2 R 3 R 123  R 1 R 23 
21. 21. 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 R 1 R 2 R 1 R 2