Last time…

1. Last time… Equipotential lines Capacitance and capacitors Physics 208 Lecture 12

2. Parallel plate capacitor -Q Geometrical factor determined from electric fields +Q Energy stored in parallel-plate capacitor Energy density d Physics 208 Lecture 12

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 12

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 12

5. -Q +Q A d Different geometries of capacitors +Q Parallel plate capacitor -Q L Spherical capacitor Cylindrical capacitor Physics 208 Lecture 12

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 Q on each is same Physics 208 Lecture 12

7. Combining Capacitors — Series VA VA C1 Q Ceq Q Vm -Q C2 Q -Q -Q VB VB Physics 208 Lecture 12

8. Physics 208 Lecture 12

9. Current in a wire: not electrostatic equilibrium • Battery produces E-field in wire • Charge moves in response to E-field Physics 208 Lecture 12

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 12

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 12

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 12

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 12

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 12

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 12

16. Resistivity • Resistivity • SI units Ω-m Independent of sample geometry Physics 208 Lecture 12

17. Resistors Circuits Physical layout Schematic layout Physics 208 Lecture 12

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 12

19. I2 I1 I3 I1=I2+I3 I1 I3 I2 I1+I2=I3 Current conservation Iin Iout Iout = Iin Physics 208 Lecture 12

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 12