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Transcript
Chapters 25.4 and 26 to 26.3 1 How current flows x 1 2 3 2 EMF—Electromotive Force Any chemical, solar, mechanical, heat method of creating a potential difference Batteries Alternator, dynamo Solarcell, photovoltaic Thermocouple Symbol E Units: volts 3 A simple circuit i 4 EMF Devices Ideal EMF device– no internal resistance Real EMF device– some internal resistance 5 Batteries Several Different Types of Batteries (called cells) Wet Cell (left) Car Batteries High Current Apps Dry Cells (Zn-Cu paste) e-e- Dry Cell Ratings PbO2 PbSO Pb 4 PbSO4 PbO2 Pb Pb H2 SO4 20 mA 80 mA 150 mA Akaline Cells PbO2 AAA AA 25 mA C D AAA AA 300 mA C D 200 mA 500 mA 600 mA EMF=1.5 V Cells are constant voltage sources: 1.5 3 6 9 12 15 24 48 V 6 Internal Resistance The battery itself can have some resistance to current flow PbO2 Pb PbO2 Pb PbO2 Pb H2 SO4 Could be terminals Could be plates or paste Could be combination 7 Internal Resistance We treat the internal resistance as if an external resistor had been added to the circuit just ahead of the positive terminal 8 Terminal Voltage (Effective Voltage) EMF R Vab=Va-Vb=EMF-iR va vb 9 Loop Rule The algebraic sum of changes in potential encountered in a complete traversal of the circuit must be zero. AKA Kirchoff’s Loop Rule Consider Dr. Womble Nashville Panama City Total Elevation Change = 0 10 From an electrical perspective 11 Resistance rule For a move through a resistor in the direction of current, the change in potential is –iR If the move opposes the current then the change in potential is +iR. move +iR Va-Vb= -iR Va i Vb 12 EMF Rule For a move from the negative terminal to the positive terminal then the change in potential is +EMF For a move from “+” to “-” then the change in potential is -EMF move -EMF +EMF 13 Putting these ideas into practice i.e changing a circuit into an equation X 1. Pick a direction for the current. 2. Pick a direction of circuit traversal 3. Sum the potentials as you traverse the circuit My move R=65 W EMF=5 V i From X, +iR+EMF=0 EMF=-iR 5=-65i i=-0.076 A or -76 mA The negative sign means that we guessed the wrong direction for the current. 14 Resistors in Series Connected resistances are said to be in series when a potential difference that is applied across their combination is the sum of the resulting potential differences across all the resistances. R3 R2 E-iR1-iR2-iR3=0 E E Req i EMF R1 R2 R3 EMF i Req R1 So Req=R1+R2+R3 15 Reducing Networks, If You Can, then DO SO! Always try to reduce the total number of variables by using the equivalent resistance. For N resistors in series, the equivalent resistance is Req=R1+R2+….+RN 16 How to find a potential difference To find the potential difference between any two points 1. 2. 3. Start at one point Traverse the circuit following any path Add algebraically the changes in potential Point A R3 i R2 Point B R1 Blue— Va –iR3-iR2=Vb Va-Vb=i(R3+R2) E Red— Va-E+iR1=Vb Va-Vb=E-iR1 17 One last word on internal resistance Recall Power, P=Vi a X r E-ir=0 Va+ir-E=Vb Va-Vb=E-ir P=iV <-(Va-Vb) P=i(E-ir) P=Ei-i2r i E b X Power of EMF Device Thermal dissipation (losses) 18 Junction Rule Sum of all currents entering a junction must equal the sum of all currents leaving the junction. i3 i1 i3 i1 i2 i2 i1+i3=i2 i1 i3 i1+i2=i3 i2 i1+i2+i3=0 IN = OUT 19 Resistors in Parallel Connected resistances are said to be in parallel when a potential difference that is applied across their combination results in that same potential difference across each resistance. i1 i E i3 E R1 R2 R3 i=i1+i2+i3 i E i2 Req V V V V Req R1 R2 R3 1 1 1 1 1 Req Req R1 R2 R3 1 1 1 R1 R2 R3 20 Resistor Color Codes Color Codes Color Black Brown Red Orange Yellow Green Blue Violet Gray White Gold Silver No Color Value 0 1 2 3 4 5 6 7 8 9 Tolerance 1% 2% 3% 4% 1 2 3 T Band1*10+Band2 x 10^ Band 3 +/- Band T 5% 10% 20% 21 Guidelines for Problem Solving Replace network of resistors with their equivalents (if possible) If you can’t simplify to a single loop, then use the junction rule and the loop rule to set up a series of equations. Be sure to: 1. 2. 1. Pick a direction of current (sign is a mathematical convention) 1. 2. If you traverse a resistor against the current then +iR else –iR If you traverse an EMF source from low potential to high potential then the EMF is positive, else negative. You have the following arbitrary choices 3. 1. 2. 3. 4. Directions of currents Which loops to use Direction of traversal of each loop Starting point and ending point ABOVE ALL, REMEMBER: 4. 1. 2. TRAVERSE THE LOOP COMPLETELY ONCE YOU HAVE CHOSEN A DIRECTION OF THE CURRENT YOU MUST STICK WITH THIS DIRECTION UNTIL YOU HAVE FINISHED THE PROBLEM. 22