Capacitors and Dielectrics: Understanding the Principles and Applications

1. Dielectrics PH 203 Professor Lee Carkner Lecture 9

2. 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

3. 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)

4. 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

5. 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

6. 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

7. 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

8. 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”

9. 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

10. 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

11. 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

12. Charging a Capacitor

13. 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

14. Next Time • Test #1 • For next Wednesday • Read 26.1-26.3 • Problems: Ch 26, P: 1, 6, 13, 15

15. Three identical capacitors are connected in parallel. If a total charge Q flows from the battery, what is the charge on each capacitor? • Q/3 • Q • 3Q • 6Q • 9Q

16. 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? • Series, lone, parallel • Parallel, series, lone • Lone, series, parallel • Parallel, lone, series • Series, parallel, lone

17. If two capacitors are in series and a third capacitor is added in series, what happens to the total charge stored? • It goes up • It goes down • It stays the same • It depends on the C value of the new capacitor • It depends on the voltage of the battery