# Lect09 - Physics 212 Today's Concept Electric Current...

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Unformatted text preview: Physics 212 Today's Concept: Electric Current Ohm’s Law & resistors, Resistors in circuits, Power in circuits 40 30 20 10 0 Lecture 9 Confused Avg = 3.4 Confident Physics 212 Lecture 9, Slide 1 Physics Announcements • Exam tomorrow at 7:00—Bring ID and check “Hour Exam Rooms” tab so you know where to go. • Familiarize yourself with exam procedures (I sent all of you an email about this last Thu) and room layouts (under “Exam Information” tab in course web page). • Exam Review today at 5:00 here. **You may want to print the review PowerPoint so you can take notes on it** It is in the “Exam Information” tab called “Exam 1 Review Lecture.” Physics 212 Lecture 9, Slide 2 Physics Key Concepts for Today: 1) How resistance depends on A, L, σ, ρ 2) How to combine resistors in series and parallel 3) Understanding resistors in circuits Today’s Plan: 1) Review of resistance & preflights 2) Work out a circuit problem in detail The good news is: This is not hard—we only have a couple of big ideas to apply and the rest is simple algebra Physics 212 Lecture 9, Slide 3 Physics I σ A L V Observables: Conductivity – high for good conductors. Ohm’s Law: J = σ E V = EL I = JA I/A=J=σV/L I = V/R I = V/(L/σΑ) R= L σA Physics 212 Lecture 9, Slide 4 Physics R = Resistance ρ = 1/σ This is just like plumbing! I is like flow rate of water V is like pressure R is how hard it is for water to flow in a pipe To make R big, make L long or A small To L R= σA To make R small, make L short or A big Physics 212 Lecture 9, Slide 5 Physics Preflight 2 Same current through both resistors Compare voltages across resistors Preflight 4 70 60 50 40 30 20 10 0 L R∝ A L V = IR ∝ A 80 60 40 20 0 A2 = 4 A1 ⇒ V2 = 1 V1 4 L2 = 2 L1 ⇒ V2 = 2V1 Physics 212 Lecture 9, Slide 6 Physics Preflight 12 BB 70 I J≡ A Same Current 60 J1 = J 3 = 2 J 2 1 J∝ A 50 40 30 20 10 0 Physics 212 Lecture 9, Slide 7 Physics Resistor Summary Series R1 R2 Parallel R1 R2 Each resistor on a different wire. Same for each resistor. Vtotal = V1 = V2 Different for each resistor Itotal = I1 + I2 Decreases 1/Req = 1/R1 + 1/R2 Physics 212 Lecture 9, Slide 8 Physics Wiring Voltage Current Resistance Each resistor on the same wire. Different for each resistor. Vtotal = V1 + V2 Same for each resistor Itotal = I1 = I2 Increases Req = R1 + R2 Adding capacitors and adding resistors is “opposite” Preflight 6 100 80 60 40 20 0 R2 in series with R3 Current through R2 and R3 is the same I 23 = V R2 + R3 Physics 212 Lecture 9, Slide 9 Physics R1 = R2 = R3 = R Preflight 7 Compare the current through R1 with the current through R2 I1/I2 = 1/2 I1/I2 = 1/3 I1/I2 = 1 I1/I2 = 2 I1/I2 = 3 Preflight 9 Compare the voltage across R2 with the voltage across R3 V2 > V3 V2 = V3 = V V2 = V3 < V V2 < V3 Preflight 10 Compare the voltage across R1 with the voltage across R2 V1 = V2 = V V1 = ½ V2 = V V1 = 2V2 = V V1 = ½ V2 = 1/5 V 1/5 V1 = ½ V2 = ½ V Physics 212 Lecture 9, Slide 10 Physics 60 50 40 30 20 10 BB R1 = R2 = R3 = R 0 Preflight 7 Compare the current through R1 with the current through R2 A I1/I2 = 1/2 B I1/I2 = 1/3 C I1/I2 = 1 D I1/I2 = 2 E I1/I2 = 3 We know: I 23 = V R2 + R3 I1 = I 23 V R1 Similarly: I1 = R2 + R3 R1 I1 R2 + R3 = =2 I 23 R1 Physics 212 Lecture 9, Slide 11 Physics BB 60 50 40 30 R1 = R2 = R3 = R 20 10 0 Preflight 9 Compare the voltage across R2 with the voltage across R3 A B C D V2 > V3 V2 = V3 = V V2 = V3 < V V2 < V3 Consider loop V23 = V V23 = V2 + V3 R2 = R3 ⇒ V2 = V3 V V2 = V3 = 2 Physics 212 Lecture 9, Slide 12 Physics BB 60 50 40 30 R1 = R2 = R3 = R 20 10 0 Preflight 10 Compare the voltage across R1 with the voltage across R2 A V1 = V2 = V B C D E V1 = ½ V2 = V V1 = 2V2 = V V1 = ½ V2 = 1/5 V 1/5 V1 = ½ V2 = ½ V R1 in parallel with series combination of R2 and R3 V 1= V23 R2 = R3 ⇒ V2 = V3 V1 = 2V2 = V Physics 212 Lecture 9, Slide 13 Physics V23 = V2 + V3 = 2V2 R1 V R2 Calculation In the circuit shown: V = 18V, R1 = 1Ω, R2 = 2Ω, R3 = 3Ω, and R4 = 4Ω. R3 R4 What is V2, the voltage across R2? • Conceptual Analysis: – – • Strategic Analysis – – – Ohm’s Law: when current I flows through resistance R, the potential drop V is given by: V = IR. Resistances are combined in series and parallel combinations • Rseries = Ra + Rb • (1/Rparallel) = (1/Ra) + (1/Rb) Combine resistances to form equivalent resistances Evaluate voltages or currents from Ohm’s Law Expand circuit back using knowledge of voltages and currents Physics 212 Lecture 9, Slide 14 Physics R1 V R2 Calculation In the circuit shown: V = 18V, R1 = 1Ω, R2 = 2Ω, R3 = 3Ω, and R4 = 4Ω. BB R3 R4 What is V2, the voltage across R2? • Combine Resistances: R1 and R2 are connected: (A) in series (B) in parallel Parallel Combination Ra (C) neither in series nor in parallel Series Combination Ra Rb Rb Parallel: Can make a loop that contains only those two resistors Series : Every loop with resistor 1 also has resistor 2. Physics 212 Lecture 9, Slide 15 Physics R1 V R2 Calculation In the circuit shown: V = 18V, R1 = 1Ω, R2 = 2Ω, R3 = 3Ω, and R4 = 4Ω. BB R3 R4 What is V2, the voltage across R2? • Combine Resistances: R2 and R4 are connected: (A) in series (B) in parallel (C) neither in series nor in parallel Series Combination Ra Rb Series : Every loop with resistor 1 also has resistor 2. Physics 212 Lecture 9, Slide 16 Physics R1 V R2 Calculation In the circuit shown: V = 18V, R1 = 1Ω, R2 = 2Ω, R3 = 3Ω, and R4 = 4Ω. BB R3 R4 What is V2, the voltage across R2? R2 and R4 are connected in series = R24 = 2 + 4 = 6 Ω • Combine Resistances: Redraw the circuit using the equivalent resistor R24 = series combination of R2 and R4. R1 V R24 V R1 R1 R3 R24 R3 V R3 R24 (A) (B) (C) Physics 212 Lecture 9, Slide 17 Physics R1 V Calculation In the circuit shown: V = 18V, R3 R1 = 1Ω, R2 = 2Ω, R3 = 3Ω, and R4 = 4Ω. R24 BB R24 = 6Ω What is V2, the voltage across R2? R2 and R4 are connected in series = R24 R3 and R24 are connected in parallel = R234 • Combine Resistances: What is the value of R234? (A) R234 = 1 Ω (B) R234 = 2 Ω (C) R234 = 4 Ω (D) R234 = 6 Ω R234 = 2 Ω (1/Rparallel) = (1/Ra) + (1/Rb) 1/R234 = (1/3) + (1/6) = (3/6) Ω−1 Physics 212 Lecture 9, Slide 18 Physics R1 V I1 = I234 Calculation In the circuit shown: V = 18V, R234 R24 = 6Ω R234 = 2Ω What is V2, the voltage across R2? R1 = 1Ω, R2 = 2Ω, R3 = 3Ω, and R4 = 4Ω. R1 and R234 are in series. R1234 = 1 + 2 = 3 Ω V = I1234 R1234 Ohm’s Law tells us I1234 = V/R1234 = 18 / 3 = 6 Amps Physics 212 Lecture 9, Slide 19 Physics Calculation V I1234 R1234 In the circuit shown: V = 18V, R1 = 1Ω, R2 = 2Ω, R3 = 3Ω, and R4 = 4Ω. BB R24 = 6Ω R234 = 2Ω I1234 = 6 A What is V2, the voltage across R2? R1 V = I1 = I234 a I234 = I1234 Since R1 in series w/ R234 R234 b V234 = I234 R234 =6x2 = 12 Volts • What is Vab, the voltage across R234 ? (A) Vab = 1 V (B) Vab = 2 V (C) Vab = 9 V (D) Vab = 12 V (E) Vab = 16 V Physics 212 Lecture 9, Slide 20 Physics Calculation R1 V V R1 R3 R234 R24 V = 18V R1 = 1Ω R 2 = 2Ω R 3 = 3Ω R4 = 4Ω. BB R24 = 6Ω R234 = 2Ω I1234 = 6 Amps I234 = 6 Amps V234 = 12V What is V2? Which of the following is/are true? A) V234 = V24 B) I234 = I24 C) Both A+B D) None Since R3 and R24 where combined in parallel to get R234 Voltages are same! Ohm’s Law I24 = V24 / R24 = 12 / 6 = 2 Amps Physics 212 Lecture 9, Slide 21 Physics Calculation R1 V V R1 R2 R3 R24 R3 R4 V = 18V R1 = 1Ω R 2 = 2Ω R 3 = 3Ω R4 = 4Ω. BB Which of the following is/are true? A) V24 = V2 B) I24 = I2 C) Both A+B D) None R24 = 6Ω R234 = 2Ω I1234 = 6 Amps I234 = 6 Amps V234 = 12V V24 = 12V I24 = 2 Amps What is V2? Since R2 and R4 where combined in series to get R24 Currents are same! Ohm’s Law V 2 = I2 R 2 = 2 x2 = 4 Volts! Physics 212 Lecture 9, Slide 22 Physics R1 V R2 Quick Follow-Ups R1 a R3 R4 = V R234 b • What is I3 ? (A) I3 = 2 A (B) I3 = 3 A (C) I3 = 4 A V = 18V R1 = 1W R2 = 2W BB R3 = 3W R4 = 4W. R24 = 6W R234 = 2W I1234 = 6 Amps I234 = 6 Amps V234 = 12V V24 = 12V I24 = 2 Amps V3 = Vab = 12V I3 = V3/R3 = 12V/3Ω = 4A I1 = I2 + I 3 Make Sense??? Note that we know I1 = I1234 = 6 A This result, that the total current entering a “node” equals the total current leaving the node, is “Kirchhoff’s current rule,” which we will study on Thursday. Physics 212 Lecture 9, Slide 23 Physics ...
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## This note was uploaded on 02/21/2011 for the course PHYS 212 taught by Professor Kim during the Spring '08 term at University of Illinois, Urbana Champaign.

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