Dielectrics PH 203 Professor Lee Carkner Lecture 9

Test 1 on Monday  Covers the whole course through today  Chapters  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 

Cylinder  For a capacitor made from two coaxial cylinders, the area is 2  rL and thus E = q/(2  0 rL)   Integrating yields: C = (2  0 )[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 4  r 2 and thus E = kq/r 2  C = (4  0 )[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, , that is multiplicative factor in the capacitance C =  0 A/d 

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  = 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  V across the plates is equal to the  V of the battery

Charging a Capacitor

Total Energy  Energy = 1/2 Q  V =1/2 C (  V) 2 = Q 2 /2C  since Q = C  V  Large C and large  V produce large stored energy 

Next Time  Test #1  For next Wednesday  Read  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)Q/3 B)Q C)3Q D)6Q E)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)Series, lone, parallel B)Parallel, series, lone C)Lone, series, parallel D)Parallel, lone, series E)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)It goes up B)It goes down C)It stays the same D)It depends on the C value of the new capacitor E)It depends on the voltage of the battery