Last time… Equipotential lines Capacitance and capacitors Thur. Oct. 9, 2007 Physics 208 Lecture 12

Parallel plate capacitor -Q Geometrical factor determined from electric fields +Q Energy stored in parallel-plate capacitor Energy density d Thur. Oct. 9, 2007 Physics 208 Lecture 12

Quick Quiz An isolated parallel plate capacitor has charge Q and potential V. The plates are pulled apart. Which describes the situation afterwards? +Q -Q + - d pull 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 Thur. Oct. 9, 2007 Physics 208 Lecture 12

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? +q -q + - d pull 1) Increases 2) Decreases 3) Stays the same Thur. Oct. 9, 2007 Physics 208 Lecture 12

Different geometries of capacitors +Q +Q -Q d A -Q L Spherical capacitor Cylindrical capacitor Parallel plate capacitor Thur. Oct. 9, 2007 Physics 208 Lecture 12

Combining Capacitors — Parallel Connect capacitors together with metal wire C1 C2 Ceq “Equivalent” capacitor Both have same V Potential difference V Need different charge Total charge Q on each is same Thur. Oct. 9, 2007 Physics 208 Lecture 12

Combining Capacitors — Series VA VA C1 Q Q Ceq Vm -Q Q C2 -Q -Q VB VB Thur. Oct. 9, 2007 Physics 208 Lecture 12

Thur. Oct. 9, 2007 Physics 208 Lecture 12

Current in a wire: not electrostatic equilibrium Battery produces E-field in wire Contract this with electrostatic equiibriium: charges not moving, all constant potential. Charge moves in response to E-field Thur. Oct. 9, 2007 Physics 208 Lecture 12

Electric Current Depends on sign of charge: Electric current = I = amount of charge per unit time flowing through a plane perpendicular to charge motion SI unit: ampere 1 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 Thur. Oct. 9, 2007 Physics 208 Lecture 12

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 Say that charges move in response to an electric field (potential difference). Thur. Oct. 9, 2007 Physics 208 Lecture 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 Ask how can this be. Constant voltage produces constant electric field - > acceleration. Thur. Oct. 9, 2007 Physics 208 Lecture 12

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 Do Knutson demo of rubber ball in array of nails. Thur. Oct. 9, 2007 Physics 208 Lecture 12

Current and drift velocity This average velocity called drift velocity This drift leads to a current Current density J Conductivity Electric field Thur. Oct. 9, 2007 Physics 208 Lecture 12

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 Thur. Oct. 9, 2007 Physics 208 Lecture 12

Resistivity Resistivity SI units Ω-m Independent of sample geometry Do temperature dependent resistance Thur. Oct. 9, 2007 Physics 208 Lecture 12

Resistors Circuits Physical layout Schematic layout Thur. Oct. 9, 2007 Make point here that energy is dissipated in the resistor due to collisions. Say it is dissipated as heat in resistors, light in light bulbs. Will see later that it is not directly proportional to current, but more current -> more dissipation -> hotter resistor or brighter light. Need this for the demos and next quizzes. Schematic layout Thur. Oct. 9, 2007 Physics 208 Lecture 12

Quick Quiz Which bulb is brighter? A B Both the same Say that light bulbs are like resistors, and that more current flowing through the bulb makes the bulb brighter. Current through each must be same Conservation of current (Kirchoff’s current law) Charge that goes in must come out Thur. Oct. 9, 2007 Physics 208 Lecture 12

Current conservation I2 Iin I1 I3 I1=I2+I3 I1 I3 Iout I2 Iout = Iin Thur. Oct. 9, 2007 Physics 208 Lecture 12

Quick Quiz B brighter than A B dimmer than A Both the same How does brightness of bulb B compare to that of A? B brighter than A B dimmer than A Both the same Say that light bulbs are like resistors, and that more current flowing through the bulb makes the bulb brighter. Battery maintain constant potential difference Extra bulb makes extra resistance -> less current Thur. Oct. 9, 2007 Physics 208 Lecture 12