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Physics 208 Lecture 11: Equipotential lines, Capacitance and Capacitors

This lecture covers the topics of equipotential lines, capacitance, and capacitors in physics. It discusses the concept of parallel plate capacitors, energy stored in capacitors, combining capacitors in parallel and series, electric current, Ohm's law, resistivity, and resistors in circuits.

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Physics 208 Lecture 11: Equipotential lines, Capacitance and Capacitors

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  1. Last time… Equipotential lines Capacitance and capacitors Physics 208 Lecture 11

  2. Parallel plate capacitor -Q Geometrical factor determined from electric fields +Q Energy stored in parallel-plate capacitor AreaA AreaA Energy density d Physics 208 Lecture 11

  3. -Q +Q d pull pull + + + + - - - - Quick Quiz An isolated parallel plate capacitor has charge Q and potential V. The plates are pulled apart. Which describes the situation afterwards? A) Charge Q has decreased B) Capacitance C has increased C) Electric field E has increased D) Voltage difference V between plates has increased E) None of these Cap. isolated  Q constant C =e0A/d  C decreases E =(Q/A)/e0 E constant V= Ed  V increases Physics 208 Lecture 11

  4. + + + + - - - - -q +q d pull pull Quick Quiz An isolated parallel plate capacitor has a charge q. The plates are then pulled further apart. What happens to the energy stored in the capacitor? 1) Increases 2) Decreases 3) Stays the same Physics 208 Lecture 11

  5. -Q +Q A d Different geometries of capacitors +Q Parallel plate capacitor -Q L Spherical capacitor Cylindrical capacitor Physics 208 Lecture 11

  6. Combining Capacitors — Parallel • Connect capacitors together with metal wire Ceq C2 C1 “Equivalent” capacitor Both have same V Potential difference V Need different charge Total charge Physics 208 Lecture 11

  7. Combining Capacitors — Series VA VA C1 Q Ceq Q Vm -Q C2 Q -Q -Q VB VB Q on each is same Physics 208 Lecture 11

  8. Physics 208 Lecture 11

  9. Current in a wire: not electrostatic equilibrium • Battery produces E-field in wire • Charge moves in response to E-field Physics 208 Lecture 11

  10. Electric Current • Electric current = I = amount of charge per unit time flowing through a plane perpendicular to charge motion • SI unit: ampere1 A = 1 C / s • Depends on sign of charge: • + charge particles: current in direction of particle motion is positive • - charge particles:current in direction of particle motion is negative Physics 208 Lecture 11

  11. Quick Quiz • An infinite number of positively charged particles are uniformly distributed throughout an otherwise empty infinite space. A spatially uniform positive electric field is applied. The current due to the charge motion A. increases with time B. decreases with time C. is constant in time D. Depends on field Constant force qE Produces constant accel. qE/m Velocity increases v(t)=qEt/m Charge / time crossing plane increases with time Physics 208 Lecture 11

  12. But experiment says… • Current constant in time • Proportional to voltage • R = resistance (unit Ohm = ) • Also written • J = current density = I / (cross-section area) •  = resistivity = R x (cross-section area) / (length) • Resistivity is independent of shape Physics 208 Lecture 11

  13. Charge motion with collisions • Wire not empty space, has various fixed objects. • Charge carriers accelerate, then collide. • After collision, charged particle reaccelerates. • Result: average “drift” velocity vd Physics 208 Lecture 11

  14. Current and drift velocity • This average velocity called drift velocity • This drift leads to a current • Current density J Conductivity Electric field Physics 208 Lecture 11

  15. What about Ohm’s law? • Current density proportional to electric field • Current proportional to current density through geometrical factor • Electric field proportional to electric potential through geometrical factor Physics 208 Lecture 11

  16. Resistivity • Resistivity • SI units Ω-m Independent of sample geometry Physics 208 Lecture 11

  17. Resistors Circuits Physical layout Schematic layout Physics 208 Lecture 11

  18. Quick Quiz Which bulb is brighter? A B Both the same Current through each must be same Conservation of current (Kirchoff’s current law) Charge that goes in must come out Physics 208 Lecture 11

  19. I2 I1 I3 I1=I2+I3 I1 I3 I2 I1+I2=I3 Current conservation Iin Iout Iout = Iin Physics 208 Lecture 11

  20. Quick Quiz How does brightness of bulb B compare to that of A? B brighter than A B dimmer than A Both the same Battery maintain constant potential difference Extra bulb makes extra resistance -> less current Physics 208 Lecture 11

  21. R R 2R = Resistors in Series • Potentials add • V = DV1 + DV2 = IR1 + IR2 = = I (R1+R2) • The equivalent resistance Req = R1+R2 • I1 = I2 = I 2 resistors in series: R  L Like summing lengths Physics 208 Lecture 11

  22. Quick Quiz What happens to the brightness of the bulb B when the switch is closed? Gets dimmer Gets brighter Stays same Something else Battery is constant voltage,not constant current Physics 208 Lecture 11

  23. R R Resistors in Parallel • DV = DV1 = DV2 • I = I1 + I2 (lower resistance path has higher current) • Equivalent Resistance R/2 Add areas Physics 208 Lecture 11

  24. Quick Quiz What happens to the brightness of the bulb A when the switch is closed? Gets dimmer Gets brighter Stays same Something else Physics 208 Lecture 11

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