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lec13_020707_-_Capacitance_II

# lec13_020707_-_Capacitance_II - Capacitance II Exam 1...

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Unformatted text preview: Capacitance II Exam 1: Thursday, Feb. 8th, 7:30 9:30 p.m. Rooms: MH 220 9 a.m. A through G GC Pet. 1 p.m. A through J GC Met. 9 a.m. H through Z & 1 p.m. K through Z MH 3rd Floor extended time (7 p.m.) Multiple Choice (no partial credit) with 1 Written Problem Equation Sheet provided, Simple calculators (similar to PHGN 100) accepted Wednesday, 7 February 2007 1 C = Q /V Parallel Plate Capacitor: Review C= V = - E d +Q o A d d E -Q 2 Energy in a Capacitor: U = 1 Q = 1 QV = 1 CV 2 2 C 2 2 Steps for solving Capacitance: 1. C = Q / V 2. Calculate charge 3. Use Gauss's Law to find the Gauss' E-field 4. Use V = - E dl to find the potential 5. Solve for capacitance Wednesday, 7 February 2007 Energy Density: C1 C2 C3 1 uE = o E 2 2 Ceq, parallel = i Ci C1 C2 C3 1 Ceq, series = i 1 Ci 2 Arbitrary Combinations of Capacitors C1 C2 C3 C4 C7 C10 Dielectrics What if an insulator (dielectric) other than air is present between between the plates? The insulator becomes polarized! C5 C6 C8 C9 C11 Edielectric So what's the bottom line? what' Wednesday, 7 February 2007 3 Wednesday, 7 February 2007 4 1 The Bottom Line on Dielectrics in Capacitors - dielectric Eo = E = Eo - Edielectric = o K Question: A capacitor is charged up, and then carefully removed from the power supply. A dielectric is then slowly inserted into this now charged, isolated capacitor. As the dielectric is inserted, the energy stored in the capacitor ... A. B. C. D. Increases Decreases Remains the same Changes in an indeterminate way When the charge remains constant, the electric field is reduced by a factor of K due to the polarization of the dielectric material. V V = - E d So potential is reduced: V = o reduced: K C= Q Q KQ So capacitance is increased: C = increased: = = KCo V (Vo K ) Vo Everything we have already learned is still valid in the presence presence of dielectrics. Just make one substitution: o = K o Permittivity of material Dielectric constant of material 5 Wednesday, 7 February 2007 Wednesday, 7 February 2007 6 Question: A. Where did that energy go? B. C. Thin air Polarizing the dielectric No way of knowing More than one Dielectric A capacitor with two different dielectrics next to each other is identical to two separate capacitors in parallel! A capacitor with two different dielectrics stacked on top of each other is identical to two separate capacitors in series! Wednesday, 7 February 2007 7 Wednesday, 7 February 2007 8 2 ...
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