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Fundamentals of Physics Chapter 27 Circuits 1. 2. 3. 4. 5. 6. 7. 8. Pumping Charges Work, Energy & Emf Current in a Single Loop Circuit Other Single Loop Circuits Potential Differences Multiloop Circuits The Ammeter & the Voltmeter RC Circuits Review & Summary Chapter Questions Exercises & Problems 2006 Physics 2112 Fundamentals of Physics Chapter 27 1 Work, Energy and emf emf Device: A source of electrical energy. Keeps one point (the + terminal) at a higher potential than the other (the terminal). Does work on charge carriers in a circuit to maintain a potential difference between two terminals. Expends an internal source of energy to do this work. dW dq The emf of a device is the work done per unit charge in moving charge from its low potential terminal to its high potential terminal. Electromotive Force 2006 Physics 2112 Fundamentals of Physics Chapter 27 2 Work, Energy and emf Emf Device in a Circuit: Transfers energy to the charge carriers moving through it. The charge carriers then transfer energy to other elements in the circuit. Direction of current 2006 B > A Physics 2112 Fundamentals of Physics Chapter 27 3 Current in a Single Loop Circuit i ? Work done by the emf device: dW dq i dt Energy expended in the resistor: i dt i 2R dt Energy conservation: = iR 2006 i R Physics 2112 Fundamentals of Physics Chapter 27 4 Current in a Single Loop Circuit Kirchhoff s Loop Rule: The algebraic sum of the changes in potential encountered in a complete traversal of any loop of a circuit must be zero. -iR Resistance Rule: Passing through a resistance in the direction of i, V = - i R; in the opposite direction +i R. emf Rule: Passing through an ideal emf from in the opposite direction V = clockwise from a: - iR = 0 counterclockwise from a: 2006 +iR- to +, V = + i = 0 Physics 2112 Fundamentals of Physics R Chapter 27 5 Checkpoint a) Direction of emf arrow at B? At point a, b, c rank: b) magnitude of current c) electric potential d) electric potential of charge carriers (greatest first) 2006 Physics 2112 Fundamentals of Physics Chapter 27 6 Two batteries in a circuit E1 E2 12 V 6V direction current flow? positive or negative work done by battery? direction of current between A amd B? Battery #1 Battery #2 current flows counterclockwise Battery #1 is doing positive work (current flows from to ) Battery #2 is having work done on it (being charged) Current flows from B to A B is at higher potential than A 2006 Physics 2112 Fundamentals of Physics Chapter 27 7 Problem Current Power Power in Each Battery generating heat charging i discharging Choose a direction for the current. Define a Kirchhoff Loop: counterclockwise starting at lower left corner. Note the potential drops around the loop: E1 i R2 Power: 2006 i R1 PR E2 i2 R 0 PB i 0.5 A Vi Physics 2112 Fundamentals of Physics Chapter 27 8 Internal Resistance Real emf Battery i r = internal resistance 2006 Physics 2112 Fundamentals of Physics Chapter 27 9 Combinations of Resistors In Series: same current through each resister. Vac = Vab + Vbc Vab = - i R1 Vbc = - i R2 Req = R1 + R2 n Req Ri i 1 Vac = - i Req 2006 Note: Req is larger than any of the combining resistors. Physics 2112 Fundamentals of Physics Chapter 27 10 Combinations of Resistors In Parallel: same potential drop across each resistor. I1 I2 Vab R1 Vab R2 I = I1 + I2 1 Req 1 Req i i 2006 1 R1 Vab Req 1 R2 n i 1 1 Ri Note: Req is smaller than any of the combining resistors. Physics 2112 Fundamentals of Physics Chapter 27 11 Checkpoint If R1 > R2 > R3, rank the three resistances according to: a) current through them b) potential difference across them, greatest first 2006 Physics 2112 Fundamentals of Physics Chapter 27 12 Series or Parallel? series parallel series parallel series None in series or parallel! 2006 Physics 2112 Fundamentals of Physics Chapter 27 13 Potential Differences in Circuits To find the potential difference between any two points, start at one point and traverse the circuit to the other, following any path, and add algebraically the changes in potential encountered. = 4.4 V, 2=2.1 v r1 = 2.3 , r2=1.8 W, r3 = 5.5 a) current I b) Potential difference between terminals of battery 1 1 2006 Physics 2112 Fundamentals of Physics Chapter 27 14 Problem V1 = ? V2 = ? 2 ground 2 2 V0 = 0 2 2 12 5 2 2 2 1 i i 2 2 1 V1 12 1 1 V1 i V2 5 V2 0 1A V0 V0 11V 4 1 V0 V0 9V 2 V2 2006 V1 Physics 2112 Fundamentals of Physics 2V Chapter 27 15 Example: Single-Loop Current Apply Kirchhoff s Loop Rule: fgabcdef: + E1 - I r1 - I R1 - I R2 - E2 - I r2 - I R3 = 0 Solve for I 2006 Physics 2112 Fundamentals of Physics Chapter 27 16 Example - plugging in values Apply Kirchhoff s Loop Rule: fgabcdef: solve for I & calculate each potential drop. I = 0.5 A grounded 2006 Physics 2112 Fundamentals of Physics Chapter 27 17 Kirchhoff s Rules for Multi-Loop Circuits Loop Rule: When any closed-circuit loop is traversed, the algebraic sum of the changes in potential must equal zero. Junction Rule: At any junction point in a circuit where the current can divide, the sum of the currents into the junction must equal the sum of the currents out of the junction. 2006 Physics 2112 Fundamentals of Physics Chapter 27 18 28-6 Multi-Loop Circuits Identify the branches in the circuit and arbitrarily assign a current to each branch: bcd: - i2 bd: + i3 bad: + i1 Apply Kirchhoff s Branch Rule: 2006 i2 = i1 + i3 (currents at junctions b and d) Physics 2112 Fundamentals of Physics Chapter 27 19 28-6 Multi-Loop Circuits Kirchhoff s Branch Rule: i2 = i1 + i3 Apply Kirchhoff s Loop Rule: badb: + E1 - i1 R1 + i3 R3 = 0 bcdb: + E2 + i2 R2 + i3 R3 = 0 badcb: + E1 - i1 R1 - i2 R2 - E2 = 0 2006 Physics 2112 Fundamentals of Physics Chapter 27 20 DC Circuit Example Method I: Equivalent Circuit i1 Find i i2 i R1 loop 1 E loop 2 E=6V R1 = 6 R2 = 4 R2 R1 and R2 are in parallel. E 1 R1 1 R2 1 6 V loop i E R2 R1 1 Req 2006 i2 i1 i 1 4 E iReq 5 12 0 1 Req i E Req loop Req 2 .4 6V 2.4 Physics 2112 Fundamentals of Physics 2.5 A Chapter 27 21 DC Circuit Example iin Method II: Kirchhoff s rules iout junct junct i i1 i2 Find i i1 i2 i loop 1 R1 V E loop 2 R2 E=6V R1 = 6 R2 = 4 0 loop E i1 R1 0 6 i1 6 0 i1 EE i2 R2 0 6 i2 4 0 i2 i 2006 i1 i2 1 1.5 1A 1. 5 A 2 .5 A Physics 2112 Fundamentals of Physics Chapter 27 22 Example 2 R1 = 20 R3 = 30 , R2 =20 , , R4 = 8.0 =12V What is current through the battery? 2006 Physics 2112 Fundamentals of Physics Chapter 27 23 Example 3 R1 = 2.0 , R2 =4.0 = 3.0 V, , = 3.0 V What is magnitude and direction of the current in the three branches? 2006 Physics 2112 Fundamentals of Physics Chapter 27 24 What are i1 and i2 ? i8 16 8 i8 i8 2006 0 2A 8 i4 4 4 16 Physics 2112 Fundamentals of Physics 4 i4 8 0 i4 2A Chapter 27 25 Meters Ammeter: Voltmeter: RA << R RV >> R Galvanometer 2006 Physics 2112 Fundamentals of Physics Chapter 27 26 RC Circuits Charging the capacitor Discharging the capacitor 2006 switch S turned to point a switch S turned to point b Physics 2112 Fundamentals of Physics Chapter 27 27 28-8 RC Circuits Charging the capacitor switch S turned to point a VR iR VC E VR VC 0 E iR q C 0 Clockwise loop: 2006 Physics 2112 Fundamentals of Physics q C Chapter 27 28 RC Circuits VR iR VC E 1st Order Linear D.E. Solution: 2006 R q C iR dq dt qt q C CE q C 0 E 1 e t RC Physics 2112 Fundamentals of Physics Chapter 27 29 RC Circuits Charging the Capacitor: q0 q qt C E 1 e t RC 0 CE R = 2000 C = 1 mF E = 10 V Time Constant = RC = 2 ms 2006 Physics 2112 Fundamentals of Physics Chapter 27 30 RC Circuits Discharging the capacitor b switch S turned to point VR iR VC Kirchhoff loop: VR iR R Solution: 2006 dq dt qt VC q C q C q C 0 0 0 q0 e t RC Physics 2112 Fundamentals of Physics Chapter 27 31 RC Circuits Discharging the capacitor qt q0 CE it 2006 q0 e t RC dq dt q0 e RC t RC Physics 2112 Fundamentals of Physics Chapter 27 32 Problem = 6.0V, 2 = 5.0V, 3 = 4.0V R1 = 100 , R2= 50 Current in each resistor? Potential difference between a and b? 1 E1 i2 E2 i2 E2 0 i1 R1 0 0 . 05 A Potential difference between points a and b? Vb E3 E2 V ab 2006 i2 R 2 0.06 A i1 i1 E3 Physics 2112 Fundamentals of Physics Va E3 E2 Chapter 27 33 This document was created with Win2PDF available at http://www.daneprairie.com. 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