lecture10_capacitors_072211

# lecture10_capacitors_072211 - Physics 142 Rank in order...

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Unformatted text preview: Physics 142 7/22/2011 Rank in order, from largest to smallest, the potential differences ∆V12, ∆V13, and ∆V23 between points 1 and 2, points 1 and 3, and points 2 and 3. 0% A. 0% B. 0% C. 0% D. 0% E. ∆V13 > ∆V12 > ∆V23 ∆V13 = ∆V23 > ∆V12 ∆V13 > ∆V23 > ∆V12 ∆V12 > ∆V13 = ∆V23 ∆V23 > ∆V12 > ∆V13 Physics 142 Summer 2011 Physics 142 Summer 2011 Equipotentials around two oppositely charged conductors Near each conductor equipotentials resemble the surface of that conductor Physics 142 Summer 2011 Dr. Nick Cummings 1 Physics 142 7/22/2011 Electric Potential From Multiple Sources If If we have multiple sources, the resulting voltage is the sum of the voltage due to each source – It comes from the work that would be done to move a test charge to that position – Work due to all charges is just the sum of the work due to each charge individually V tot = ∑V j j Physics 142 Summer 2011 Potential for two point charges Physics 142 Summer 2011 Electric Potential, Energy, and Motion Emech = U + KE = qV + 1 mv 2 2 Since Since total energy remains constant, increase in potential means a decrease in kinetic energy – And vice versa We We can determine many things about the motion of charges through an electric field using this consideration Physics 142 Summer 2011 Dr. Nick Cummings 2 Physics 142 7/22/2011 Physics 142 Summer 2011 Physics 142 Summer 2011 Physics 142 Summer 2011 Dr. Nick Cummings 3 Physics 142 7/22/2011 Batteries Batteries Batteries use a chemical reaction to move charges from one side to another – Electrolyte in the battery has ions free to move – Different metals at each end , electrodes – One reaction requires extra electrons (reduction) – One reaction produces extra electrons (oxidation) – These reactions create a potential difference between the terminals Physics 142 Summer 2011 Batteries Voltage Voltage difference is created between the ends (“terminals”) of the battery » High voltage: + terminal or cathode » Low voltage: – terminal or anode Since Since inside the battery electrons are moved from the + to – this takes work – Energy is provided by a chemical reaction » Comes from molecular binding energy – Called an emf emf » emf = ∆U/q Physics 142 Summer 2011 Gravitational Batteries What would be the gravitational analog? Something Something like an escalator that hauls mass up to a higher point using energy from another source (electricity in that case) Physics 142 Summer 2011 Dr. Nick Cummings 4 Physics 142 7/22/2011 Batteries An An idealized battery maintains a constant voltage between the terminals – Batteries are usually labels with this voltage (e.g. 9 V battery) » AA & AAA are 1.5 V – Various factors may make voltage vary a bit in practice Physics 142 Summer 2011 What total potential difference is created by these three batteries? 1.0 V 2.0 V C. 5.0 V D. 6.0 V E. 7.0 V 0% A. 0% B. 0% 0% 0% Physics 142 Summer 2011 Kirchhoff’s Loop Rule We We said changing voltage is analogous to going up and down hill in gravity When When you go in a closed loop, you always come back to the same height to started at ∑ ∆V i =0 loop Physics 142 Summer 2011 Dr. Nick Cummings 5 Physics 142 7/22/2011 Storing electrical energy: The capacitor Two Two parallel metal plates of area A separated by a distance d. Connect Connect the plates to the two sides of a battery. E + + + + + + + – – – – – – – V 0 Physics 142 Summer 2011 Charging a capacitor What What is the potential difference between the plates? What What is the field around the plates? How How much charge is on each plate? E + + + + + + + V – – – – – – – 0 Physics 142 Summer 2011 Capacitor Equations ∆V = Ed E= η Q/ A = ε0 ε0 Q ∆V = ε A d 0 ε A Q = 0 ∆V d Q = C∆V What does this “Q” stand for? Dr. Nick Cummings Physics 142 Summer 2011 6 Physics 142 7/22/2011 Capacitance Q = C∆V C is called the capacitance is This This is how easy it is to charge up the capacitor • Bigger C means bigger Q for the same ∆V Capacitor Capacitor stores electrical energy Q∆V Unit Unit of capacitance is the Faraday – 1 F = 1 C/V Physics 142 Summer 2011 Cap #1 is charged by connecting it to a battery. Cap #2 is not charged. C#1 is disconnected from the battery and connected to C#2. How does the magnitude of the E field in C#1 change? 0%1. 0%2. 0%3. 0%4. 0%5. 0% 6. Same Bigger by ~X2 Bigger but not by ~X2 Smaller by ~X2 Smaller but not by ~X2 Can’t tell Physics 142 Summer 2011 Three capacitors 1, 2, 3 are connected to identical batteries so they each have the same ∆V. Their plate areas and separations are as follows: A2 = 2 A1 = 2 A3; d1 = d2 = 2d3. How do the E fields inside them rank? 0% 1. 1. 0% 2. 0% 3. 0% 4. 0% 5. 0% 6. E2 = E3 > E1 E3 > E1 = E2 E2 > E1 > E3 E2 > E1 = E3 E1 = E2 > E3 Other Physics 142 Summer 2011 Dr. Nick Cummings 7 Physics 142 7/22/2011 Physics 142 Summer 2011 Dr. Nick Cummings 8 ...
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