Transcript Dielectrics
Dielectrics PH 203 Professor Lee Carkner Lecture 9 Test 1 on Monday Covers the whole course through today Chapters 21-25 10 multiple choice (20 points) 4 problems (20 points each) Equations and constants given but not labeled Bring calculator No PDA’s, no cellphones, no sharing Study PAL’s Notes Homework Other Capacitors We can find C by solving V = ∫ E ds for a path between the plates If we do this we find: Capacitance only depends on the geometry of the plate arrangement (and e) Cylinder For a capacitor made from two coaxial cylinders, the area is 2prL and thus E = q/(2pe0rL) Integrating yields: C = (2pe0)[L / ln (b/a)] Where “ln” is the natural log, a is the radius of the inner cylinder and b is the radius of the outer Sphere For a capacitor made from two concentric spherical shells, the area is 4pr2 and thus E = kq/r2 C = (4pe0)[ab/(b-a)] Note for a single sphere: Where R is the sphere radius Between the Plates In our treatment of the capacitor we assumed the space between the plates was filled with air Each material has a dielectric constant, k, that is multiplicative factor in the capacitance C = ke0A/d k Dielectric The polarized material partially cancels out the electric field between the plates reducing the voltage A dielectric allows a capacitor to store more charge with the same voltage Dielectric Constant The dielectric constant is always greater than one It is the number of times greater the capacitance is compared to the air filled case e.g. if we add a capacitor with k = 2 we double the capacitance and the charge stored for a given voltage Prevents “shorting out” Breakdown The dielectric must be an insulator If the voltage is large enough, the charge will jump across anyway While Q = CV, there is a limit to how much we can increase Q by increasing V When the voltage is too high and the capacitor shorts through the dielectric, it is called breakdown Dielectric Strength The field between the plates however depends on the voltage applied and the plate separation, d E = V/d Decrease the voltage Increase the plate separation Energy in a Capacitor Every little batch of charge increases the potential difference between the plates and increases the work to move the next batch Charge stops moving when the DV across the plates is equal to the DV of the battery Charging a Capacitor Total Energy Energy = 1/2 Q DV =1/2 C (DV)2 = Q2/2C since Q = C DV Large C and large DV produce large stored energy Next Time Test #1 For next Wednesday Read 26.1-26.3 Problems: Ch 26, P: 1, 6, 13, 15 Three identical capacitors are connected in parallel. If a total charge Q flows from the battery, what is the charge on each capacitor? A) B) C) D) E) Q/3 Q 3Q 6Q 9Q Consider two capacitors in series with a battery, two capacitors in parallel with a battery and a lone capacitor connected directly to a battery. If all the capacitors and batteries are identical, which ranks the situations from most to least charge stored? A) B) C) D) E) Series, lone, parallel Parallel, series, lone Lone, series, parallel Parallel, lone, series Series, parallel, lone If two capacitors are in series and a third capacitor is added in series, what happens to the total charge stored? A) B) C) D) It goes up It goes down It stays the same It depends on the C value of the new capacitor E) It depends on the voltage of the battery