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Transcript
Physics 102: Lecture 05 Circuits and Ohm’s Law • Today’s lecture will cover Textbook sections 18.4,.6, 8 Practice exams available on course webpage under “Course Info” Homework, keep lots of digits! Physics 102: Lecture 5, Slide 1 Last Time • Capacitors – – – – Physical Series Parallel Energy C = e0A/d 1/Ceq = 1/C1 + 1/C2 Ceq = C1 + C2 U = 1/2 QV Today • Resistors – – – – Physical Series Parallel Power Physics 102: Lecture 5, Slide 2 R = r L/A Req = R1 + R2 1/Req = 1/R1 + 1/R2 P = IV Electric Terminology • Current: Moving Charges – Symbol: I – Unit: Amp Coulomb/second – Count number of charges which pass point/sec • Power: Energy/Time – Symbol: P – Unit: Watt Joule/second = Volt Coulomb/sec – P = IV Physics 102: Lecture 5, Slide 3 Physical Resistor • Resistance: Traveling through a resistor, electrons bump into things which slows them down. R = r L /A A – r: – L: – A: L • Ohms Law I = V/R – Double potential difference double current Physics 102: Lecture 5, Slide 4 Preflight 5.1 Two cylindrical resistors are made from the same material. They are of equal length but one has twice the diameter of the other. 1. R1 > R2 2. R1 = R2 3. R1 < R2 Physics 102: Lecture 5, Slide 5 1 2 Preflight 5.1 Two cylindrical resistors are made from the same material. They are of equal length but one has twice the diameter of the other. 1. R1 > R2 2. R1 = R2 3. R1 < R2 Physics 102: Lecture 5, Slide 6 R = ρ L/A 1 2 Comparison: Capacitors vs. Resistors • Capacitors store energy as separated charge: U=1/2QV – Capacitance: ability to store separated charge: C = ke0A/d – Voltage determines charge: V=Q/C • Resistors dissipate energy as power: P=VI – Resistance: how difficult it is for charges to get through: R = r L /A – Voltage determines current: V=IR • Don’t mix capacitor and resistor equations! Physics 102: Lecture 5, Slide 7 Simple Circuit I e • Practice… R I – Calculate I when e = 24 Volts and R = 8 W Physics 102: Lecture 5, Slide 8 Simple Circuit I • Visualization • Practice… e – Calculate I when e=24 Volts and R = 8 W – Ohm’s Law: V =IR I = V/R Physics 102: Lecture 5, Slide 9 = 3 Amps R I Resistors in Series • One wire: – Effectively adding lengths: • Req=r(L1+L2)/A – Since R L, add resistance: R = Req = R1 + R2 R Physics 102: Lecture 5, Slide 10 2R Resistors in Series • Resistors connected end-to-end: – If current goes through one resistor, it must go through other. I1 = I2 = Ieq – Both have voltage drops: V1 + V2 = Veq Req = Veq = V1 + V2 = R1 + R2 Ieq Ieq Physics 102: Lecture 5, Slide 11 R1 Req R2 Preflight 5.3 Compare I1 the current through R1, with I10 the current through R10. 1. I1 < I10 2. I1 = I10 3. I1 > I10 R1=1W e 0 R10=10W ACT: Series Circuit Compare V1 the voltage across R1, with V10 the voltage across R10. 1. V1>V10 Physics 102: Lecture 5, Slide 12 2. V1=V10 3. V1<V10 Preflight 5.3 R1=1W Compare I1 the current through R1, with I10 the current through R10. 1. I1<I10 2. I1=I10 3. I1>I10 e 0 R10=10W Note: I is the same everywhere in this circuit! ACT: Series Circuit Compare V1 the voltage across R1, with V10 the voltage across R10. 1. V1>V10 2. V1=V10 3. V1<V10 Physics 102: Lecture 5, Slide 13 V1 = I1 R1 = 1 x I V10 = I10 R10 = 10 x I Practice: Resistors in Series R1=1W e0 R2=10W Calculate the voltage across each resistor if the battery has potential V0 = 22 volts. Simplify (R1 and R2 in series): • R12 = • V12 = • I12 = e0 R12 Expand: •V1 = •V2 = Check: V1 + V2 = V12 ? Physics 102: Lecture 5, Slide 14 R1=1W e0 R2=10W Practice: Resistors in Series R1=1W e0 R2=10W Calculate the voltage across each resistor if the battery has potential V0= 22 volts. Simplify (R1 and R2 in series): •R12 = R1 + R2 •V12 = V1 + V2 •I12 = I1 = I2 = 11 W = V0 = 22 Volts = V12/R12 = 2 Amps e0 R12 Expand: •V1 = I1R1 •V2 = I2R2 = 2 x 1 = 2 Volts = 2 x 10 = 20 Volts Check: V1 + V2 = V12 ? Physics 102: Lecture 5, Slide 15 YES! R1=1W e0 R2=10W Resistors in Parallel • Two wires: – Effectively adding the Area – Since R a 1/A add 1/R: 1/Req = 1/R1 + 1/R2 R Physics 102: Lecture 5, Slide 16 R = R/2 Resistors in Parallel • Both ends of resistor are connected: – Current is split between two wires: I1 + I2 = Ieq – Voltage is same across each: V1 = V2 = Veq 1 = Ieq = I1 + I2 = 1 + 1_ R1 Req Veq Veq R1 R2 Physics 102: Lecture 5, Slide 17 R2 Req Preflight 5.5 What happens to the current through R2 when the switch is closed? • Increases • Remains Same • Decreases ACT: Parallel Circuit What happens to the current through the battery? (1) Increases (2) Remains Same (3) Decreases Physics 102: Lecture 5, Slide 18 Preflight 5.5 What happens to the current through R2 when the switch is closed? • Increases • Remains Same • Decreases V2 = ε = I2R2 ACT: Parallel Circuit What happens to the current through the battery? (1) Increases (2) Remains Same Ibattery = I2 + I3 (3) Decreases Physics 102: Lecture 5, Slide 19 Practice: Resistors in Parallel e R2 R3 Determine the current through the battery. Let E = 60 Volts, R2 = 20 W and R3=30 W. Simplify: R2 and R3 are in parallel 1/R23 = 1/R2 + 1/R3 V23 = V2 = V3 I23 = I2 + I3 Physics 102: Lecture 5, Slide 20 e R23 Practice: Resistors in Parallel e R2 R3 Determine the current through the battery. Let E = 60 Volts, R2 = 20 W and R3=30 W. Simplify: R2 and R3 are in parallel 1/R23 = 1/R2 + 1/R3 R23 = 12 W V23 = V2 = V3 = 60 Volts I23 = I2 + I3 Physics 102: Lecture 5, Slide 21 e = V23 /R23 = 5 Amps R23 ACT: Your Kitchen Johnny “Danger” Powells uses one power strip to plug in his microwave, coffee pot, space heater, toaster, and guitar amplifier all into one outlet. 25 A 10 A Toaster 5A Coffee Pot 10 A Microwave This is dangerous because… (By the way, power strips are wired in parallel.) 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. Physics 102: Lecture 5, Slide 22 ACT: Your Kitchen Johnny “Danger” Powells uses one power strip to plug in his microwave, coffee pot, space heater, toaster, and guitar amplifier all into one outlet. 25 A 10 A Toaster 5A Coffee Pot 10 A Microwave This is dangerous because… (By the way, power strips are wired in parallel.) 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. Physics 102: Lecture 5, Slide 23 Summary Series Parallel R1 R1 R2 R2 Wiring Each resistor on the same wire. Each resistor on a different wire. Voltage Different for each resistor. Vtotal = V1 + V2 Same for each resistor. Vtotal = V1 = V2 Current Same for each resistor Itotal = I1 = I2 Different for each resistor Itotal = I1 + I2 Increases Req = R1 + R2 Decreases 1/Req = 1/R1 + 1/R2 Resistance Physics 102: Lecture 5, Slide 24 Preflight 5.6, 5.7 1 Which configuration has the smallest resistance? 1 2 3 Which configuration has the largest resistance? Physics 102: Lecture 5, Slide 25 2 3 Preflight 5.6, 5.7 1 R 2 2R Which configuration has the smallest resistance? 1 2 3 Which configuration has the largest resistance? 2 Physics 102: Lecture 5, Slide 26 3 R/2 Parallel + Series Tests • Resistors R1 and R2 are in series if and only if every loop that contains R1 also contains R2 • Resistors R1 and R2 are in parallel if and only if you can make a loop that has ONLY R1 and R2 • Same rules apply to capacitors!! Physics 102: Lecture 5, Slide 27 See you next lecture! • Read 18.5, 7 Physics 102: Lecture 5, Slide 28