Lect10 - Physics 212 Today's Concept Kirchhoff’s Rules...

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Unformatted text preview: Physics 212 Today's Concept: Kirchhoff’s Rules Circuits with resistors & batteries 35 30 25 20 15 10 5 0 Lecture 10 Confused Avg = 3.3 Confident Physics 212 Lecture 10, Slide 1 Physics • Help me to stop passing so much gas. • How to know if something is a drop or a gain in voltage and what exactly that means. • How to set up multi-loop problems. • I want to know my grade on my test. I want an A even though I probably wont get it because i suck at ur physics tests theyre too hard • embarrassing stories about the professor's childhood • I wonder why this exam is much more difficult than the past exams for previous 5 semesters • I don't understand one bit about the what sign or how much current flows through the blue wire from a to b. Help please • Bears. Beets. Battlestar Galactica. Physics 212 Lecture 10, Slide 2 Physics Your comments on “what do you want to learn more about? • Why was the exam as hard as it was? It was NOTHING like the past hour exams, both in difficulty and types of questions. Reminded me of the Spring 2007 211 exam #2...I believe the average was about 60%. When I tried it, I just decided to stop because it was just an order of magnitude more difficult than any of the others. Seriously, not cool of you to pull on us...I hope this wasn't about the cheating. It's terrible to make a test so unreasonably hard (and cause so much trouble for our grades) just to keep 2 people from cheating on it. IGNORING THAT... I'm ok with the circuits. Can't wait to start the homework. I really like Kirchoff's Laws. Will we have to deal with Wheatstone bridges and other evil things along those lines? • Altgeld people: Sorry. Look for an email from me about what we will do. Physics 212 Lecture 10, Slide 3 Physics Your comments on “what do you want to learn more about? Key Concepts: 1) Understanding Kirchoff’s Rules 2) Using Kirchoff’s Rules Today’s Plan: • • • Summary of Kirchoff’s rules Example problem Review Preflights Physics 212 Lecture 10, Slide 4 Physics Last Time Resistors in series: Current through is same. Voltage drop across is IRi Reffective = R1 + R 2 + R3 + ... Resistors in parallel: Voltage drop across is same. Current through is V/Ri 1 Reffective 1 1 1 =+ + + ... R1 R2 R3 Solved Circuits R1 V R2 R3 R4 = V I1234 R1234 Physics 212 Lecture 10, Slide 5 Physics 5 New Circuit R1 R3 V1 V2 R2 How Can We Solve This One? R1 V1 V2 R3 R2 V I1234 = R12 THE ANSWER: Kirchhoff’s Rules Physics 212 Lecture 10, Slide 6 Physics 5 Kirchoff’s Voltage Rule ∑ ΔV i =0 Kirchoff's Voltage Rule states that the sum of the voltage changes caused by any elements (like wires, batteries, and resistors) around a circuit must be zero. If we model voltage as height above the ground floor, see if you can come up with the analogy to Kirchoff's Voltage Rule in terms of someone walking around in the hallways and stairways and elevators of a high-rise building. If we start at the ground floor with a potential of 0, and walk around up and down stairs, take the elevator a few flights, go to the roof, parachute off, and end up back on the ground floor, our potential is still 0. Therefore, the potential difference is 0. We may have increased and decreased our potential as we traveled through the building, but we still start and end at a potential of 0. OR: The potential difference between a point and itself is zero ! Physics 212 Lecture 10, Slide 7 Physics Kirchoff’s Current Rule ∑I in = ∑ I out Kirchoff's Current Rule states that the sum of all currents entering any given point in a circuit must equal the sum of all currents leaving the same point. If we model electrical current as water, see if you can come up with an analogy to Kirchoff's Current Rule in terms of household plumbing. If you have a main water line coming into your house, it will split off to service all utilities, such as sink, toilet, shower, etc. The water in all of those lines must equal the amount of water coming out of the main line, and when all the household water drains out of the house into a main line again, all the smaller lines must include as much water as the drain carries out. OR: Electric Charge is Conserved Physics 212 Lecture 10, Slide 8 Physics Kirchhoff’s Laws (1) Label all currents Choose any direction R1 I1 (2) Label +/- for all elements Current goes + ⇒ - (for resistors) A + + 1 + R2 3 + I4 (3) Choose loop and direction Must start on wire, not element. B I2 I3 R3 R5 2 + - + - R4 (4) Write down voltage drops + First sign you hit is sign to use. Iin = Iout + I5 (5) Write down node equation We’ll do calculation first today It’s actually the easiest thing to do !! Physics 212 Lecture 10, Slide 9 Physics 17 Preflight 3 DROP BB GAIN N AI G A B C D E 60 50 40 30 With the current Against the current VOLTAGE DROP VOLTAGE GAIN + - 20 10 0 Physics 212 Lecture 10, Slide 10 Physics 1Ω 2Ω 1Ω 2V 1V 1V I2 Calculation In this circuit, assume Vi and Ri are known. What is I2 ?? • Conceptual Analysis: – •Strategic Analysis – – – Circuit behavior described by Kirchhoff’s Rules: • KVR: ΣVdrops = 0 • KCR: ΣIin = ΣIout Write down Loop Equations (KVR) Write down Node Equations (KCR) Solve Physics 212 Lecture 10, Slide 11 Physics R1 ++ V1 - I1 I2 I3 Calculation In this circuit, assume Vi and Ri are known. What is I2 ?? R2 + -+ V2 - R3 ++ V3 - Label and pick directions for each current Label the + and – side of each element This is easy for batteries For resistors, the “upstream” side is + Now write down loop and node equations Physics 212 Lecture 10, Slide 12 Physics R1 ++ V1 - I1 I2 I3 Calculation In this circuit, assume Vi and Ri are known. What is I2 ?? BB R2 + -+ V2 - R3 ++ V3 - • How many equations do we need to write down in order to solve for I2? (A) 1 • Why?? – – (B) 2 (C) 3 (D) 4 (E) 5 We have 3 unknowns: I1, I2, and I3 We need 3 independent equations to solve for these unknowns Physics 212 Lecture 10, Slide 13 Physics R1 ++ V1 - I1 I2 I3 Calculation BB R2 + -+ V2 - In this circuit, assume Vi and Ri are known. What is I2 ?? R3 ++ V3 - • Which of the following equations is NOT correct? (A) (B) (C) (D) I2 = I1 + I3 - V1 + I1R1 - I3R3 + V3 = 0 - V3 + I3R3 + I2R2 + V2 = 0 - V2 – I2R2 + I1R1 + V1 = 0 – – (D) is an attempt to write down KVR for the top loop Start at negative terminal of V2 and go clockwise • Vgain (-V2) then Vgain (-I2R2) then Vgain (-I1R1) then Vdrop (+V1) Physics 212 Lecture 10, Slide 14 Physics • Why?? R1 R2 R3 V1 V2 V3 I1 I2 I3 Calculation In this circuit, assume Vi and Ri are known. What is I2 ?? We need 3 equations: Which 3 should we use? A) Any 3 will do B) 1, 2, and 4 C) 2, 3, and 4 BB • We have the following 4 equations: 1. 2. 3. 4. I2 = I1 + I 3 - V1 + I1R1 - I3R3 + V3 = 0 - V3 + I3R3 + I2R2 + V2 = 0 - V2 – I2R2 - I1R1 + V1 = 0 – – – • Why?? We need 3 INDEPENDENT equations Equations 2, 3, and 4 are NOT INDEPENDENT • Eqn 2 + Eqn 3 = - Eqn 4 We must choose Eqn 1 and any two of the remaining ( 2, 3, and 4) Physics 212 Lecture 10, Slide 15 Physics R1 R2 R3 V1 V2 V3 I1 I2 I3 Calculation In this circuit, assume Vi and Ri are known. What is I2 ?? • We have 3 equations and 3 unknowns. I 2 = I1 + I3 V1 + I1R1 - I3R3 + V3 = 0 V2 – I2R2 - I1R1 + V1 = 0 R 2R R 2V V V I1 I2 I3 •The solution will get very messy! Simplify: assume V2 = V3 = V V1 = 2V R1 = R3 = R R2 = 2R Physics 212 Lecture 10, Slide 16 Physics Calculation: Simplify In this circuit, assume V and R are known. R 2R R 2V V V I1 I2 I3 What is I2 ?? • We have 3 equations and 3 unknowns. I 2 = I1 + I3 -2V + I1R - I3R + V = 0 (outside) -V – I2(2R) - I1R + 2V= 0 (top) • With this simplification, you can verify: I2 = ( 1/5) V/R I1 = ( 3/5) V/R I3 = (-2/5) V/R Physics 212 Lecture 10, Slide 17 Physics Follow-Up R 2R a b 2V V V I1 I2 I3 • We know: R I2 = ( 1/5) V/R I1 = ( 3/5) V/R I3 = (-2/5) V/R BB • Suppose we short R3: What happens to Vab (voltage across R2?) R Why? Redraw: 2R a b (A) Vab remains the same (B) Vab changes sign (C) Vab increases (D) Vab goes to zero 2V V V I1 I2 I3 d Vcd = +V Vbd = +V Vad = Vcd = +V c Vab = Vad – Vbd = V – V = 0 Physics 212 Lecture 10, Slide 18 Physics a b BB V R R Is there a current flowing between a and b ? A) Yes B) No A & B have the same potential Current flows from battery and splits at A No current flows between A & B Some current flows down Some current flows right Physics 212 Lecture 10, Slide 19 Physics Preflight 5 I1 I2 BB I4 I I3 I1R – I2 (2R) = 0 I4R – I3 (2R) = 0 I1 = 2 I 2 I4 = 2 I3 (1) (2) 60 50 40 30 20 10 0 Now collapse a & b into one pt & KCR gives: I1 + I2 = I3 + I4 Substitute from eqns (1) and (2): I2 = I3 KCR at node “a” gives: I1 = 2 I 3 I = I1 - I3 = 2I3 –I3 = +I3 Physics 212 Lecture 10, Slide 20 Physics Prelecture Preflight What is the same? Current flowing in and out of the battery 2R 3 2R 3 What is different? Current flowing from a to b Physics 212 Lecture 10, Slide 21 Physics I 2/ I 3 1/ I 3 R a R 2R b V 2/ I 3 V/2 2R 1/ I 3 2/ I 3 2 1/ I 3 1/ I 3 1/ I 0 3 1/ I 3 2/ I 3 Physics 212 Lecture 10, Slide 22 Physics Preflight 7 IA IB BB c c 60 Current will flow from left to right in both cases In both cases, Vac = V/2 = I2R (2R) = I4R (4R) I2R = 2I4R IA = IR – I2R = IR – 2I4R IB = IR – I4R 50 40 30 20 10 0 Physics 212 Lecture 10, Slide 23 Physics Model for Real Battery: Internal Resistance + r V0 R VL V0 r R VL Usually can’t supply too much current to the load without voltage “sagging” Physics 212 Lecture 10, Slide 24 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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