Electricity and MagnetismCharge DensityCharge and PotentialCharge and PotentialCapacitanceCapacitanceCapacitorParallel Plate CapacitorParallel Plate CapacitorParallel Plate CapacitorCapacitorEnergy stored in CapacitorEnergy stored in CapacitorIn-Class DemoIn-Class DemoIn-Class DemoIn-Class DemoIn-Class DemoEnergy vs VIn-Class Demo (same, but more)How much Energy is 800J ?Where is the energy stored?Where is the energy stored?Electric CircuitsElectric CircuitsElectric CircuitsElectric CircuitsMar 6 2002Electricity and Magnetism• Capacitors– Energy storage– Electric circuitsMar 6 2002Charge Density ++++++++++++++++Local radius of curvatureApplication: Lightning rod -Biggest E near pointy tip!In-Class Demo:Mar 6 2002Charge and Potential+++++++R+++++++++---------dCharged SphereParallel PlateCapacitorV=1/(4 π ε0R) QV= d/(A ε0) QGeometry!Mar 6 2002Charge and Potential• For given geometry, Potential and Charge proportional•Define – Q = C V -> C is Capacitance• Measured in [F] = [C/V] : FaradMar 6 2002CapacitanceQQVslope = 1/CC bigC smallslope = CC bigC smallVQ = C*V => V = Q/CMar 6 2002CapacitanceQslope = CC bigC smallQ2VQ1V0C bigger -> Can store more Charge!Mar 6 2002Capacitor•Def: Two conductors separated by insulator• Charging capacitor:– take charge from one of the conductors and put on the other– separate + and - chargesMar 6 2002Parallel Plate Capacitor+++++++++++-----------d-Q+Q• To store lots of charge–make A big– make d smallMar 6 2002Parallel Plate Capacitor+++++++++++-----------• In-Class Demo– Charge Capacitor– Change d-Q+QdMar 6 2002Parallel Plate Capacitorslope = 1/CVC=ε0A/dd smalld big•Change d–change C• Q constantV1V2Q0Qd bigger -> C smaller -> V bigger for fixed QMar 6 2002Capacitor•By increasing d, V increased– Where does energy come from?• I have to do work to separate plates!• Let’s look at energy stored on Capacitor...Mar 6 2002Energy stored in CapacitorMar 6 2002Energy stored in Capacitor• Can store more energy, if–Cbigger– V biggerMar 6 2002In-Class DemoVabMar 6 2002In-Class DemoVabMar 6 2002In-Class DemoVabMar 6 2002In-Class DemoVabMar 6 2002In-Class DemoVab=100 VC = 1000µFU=0.5 *10-3*1002= 5 JMar 6 2002Energy vs VU[J]U = ½ C V2100V [V]200 30010204030Mar 6 2002In-Class Demo (same, but more)C = 100µFVab=4000 VU= 800 Jthin wireMar 6 2002How much Energy is 800J ?•Cyclist– Power p ~200 W => 800 J = 200 W * 4 sec•Food– 500 ‘calories’ => 500*4kJ = 2*106J– should keep you going for 2*106J/200W = 10000 sec = 3h– sounds about right...Mar 6 2002Where is the energy stored?+++++++++++------------Q+QdMar 6 2002Where is the energy stored?+++++++++++-----------• Energy is stored in Electric Field• U = ½ e0E2*Volume• E2gives Energy Density:• U/Volume = ½ e0E2+Q -QdMar 6 2002Electric CircuitsCapacitorCWireVVoltage source (like LVPS)Mar 6 2002Electric Circuits• V14provided by some source (like LVPS) • V12 = 0, because wire is conductor -> V constant• V34 = 0• V23 = V14 (after capacitor is charged)CV141423Mar 6 2002Electric Circuits• Two capacitors in parallel • V56= V23 = V14 (after capacitor is charged)• Q1/C1= Q2/C2= V14• Qtot= Q1 +Q2• Ctot= (Q1 +Q2 )/ V14 = C1+C2• Capacitors in parallel -> Capacitances add!V14C11423C256Mar 6 2002Electric Circuits• Two capacitors in series• V14= V23 + V56 • Q = Q1= Q2• Vtot= Q1/C1 +Q2/C2 = Q/(C1+C2)• 1/Ctot = 1/C1+1/C2• Inverse Capacitances
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