1. Capacitance

2. Characteristics of a Capacitor + + + + + + - - - - - - - - - - - - No Dielectric Uniform Electric Field d Area Note: Net charge of the system is zero. Charge = -q Charge = +q

3. - - - - - - - - - - - + + + + + + + + + Electric Field of a Parallel Plate Capacitor Note that the electric field between the two plates is the sum of the electric fields due to each plate individually B E+E+ E+E+ A E+E+ E-E- E-E- E-E- C E A = ½ E + + -½ E - = 0 E B = ½ E + + ½ E - = E E C = -½ E + + ½ E - = 0

4. Electric Field of a Parallel Plate Capacitor From Gauss’ Law: E = q/ε o A where: ε o = permittivity of free space = 8.854 x 10 -12 C 2 /Nm 2 A = Area of the plate - - - - - - - - - - - + + + + + + + + + E

5. Electric Field of a Parallel Plate Capacitor Since: E = ΔV/d And E = q/ε o A Set them equal to each other and rearrange to get: - - - - - - - - - - - + + + + + + + + + E The ratio of charge per volt for any capacitor is call its capacitance C. C =

6. Capacitance Capacitance is a proportionality constant that is proportional to the charge (q) between two oppositely charged objects and is inversely proportional to the potential difference between them (V). C = q/ΔV SI Units: 1 Farad = 1 Coulomb/1 Volt. A capacitor is an electrical device whose purpose is to store electrical energy which can be used in a controlled manner over a short period of time. A capacitor consists of two conductors placed near one another without touching. One is charged +q while the other is charged –q. Capacitance is an intrinsic property of the capacitor independent of charge and voltage.

7. Charging a Capacitor When a capacitor is subjected to an electric potential across its terminals, the electrons will move accordingly. When charging a capacitor, it will initially behave much like a wire, allowing very high current flow with a very small potential drop. When a capacitor nears the electric potential of the external source, the current flow will slow and eventually come to a halt. Charging and discharging a capacitor.

8. http://www.absorblearning.com/media/attachment.action?quick=qq&att=1915

9. The Dielectric The electric field resulting from a dielectric is weaker than it would be if there was nothing there. - - - - - - - - - - - - Dielectric with dipole characteristics Uniform Electric Field -+-+ -+-+ -+-+ -+-+ -+-+ -+-+ -+-+ -+-+ -+-+ -+-+ -+-+ -+-+ -+-+ -+-+ -+-+ -+-+ -+-+ -+-+ -+-+ -+-+ -+-+ -+-+ -+-+ -+-+ + + + + + +

10. The Dielectric Constant A dielectric is an insulating material that contains permanent dipole moments. Where: E o = Electric field without a dielectric medium. E = Electric field with dielectric. E o > E such that κ > 1. What does this mean? When an insulating material is added to the space between two charged plates, the electric field is decreased.

11. Effects of Adding Dielectric Material When dielectric material is added to the space between the two plates of a capacitor: The electric field intensity will decrease. The amount of charge on each of the plates will increase. The capacitance will increase.

12. Storing Electric Charge on a Parallel Plate Capacitor When a 1.2  F capacitor has a slab of dielectric material, 2.6x10 -5 C of additional charge flows onto the plates. What is the dielectric constant? q o = C o V q = κC o V The extra charge equals Δq = q – q o q – q o = κC o V – C o V ++++++++++++++++++++++++++++++ ------------------------------ + V = 12V C = 1.2F q = 2.6x10 -5 C = + 1 κ q – q o C o V Note that the excess charge that the capacitor can store is exactly equal to the charge without the dielectric times the dielectric constant. 2.8 Leads to

13. Effect of Dielectric on Voltage when q is Constant A capacitor is charged up by connecting to a battery. It is then disconnected, and a slab of dielectric material is inserted between the two plates. Does the voltage between the plates… 1. increase? 2. decrease? 3. remain the same? Why? Because q is fixed and q = CV. Since C increases with addition of the dielectric, V must decrease.

14. Applications for Parallel Plate Capacitors Microphones Keyboards RAM Starters for electric motors Electronic noise filtering applications

15. Capacitors in Series and Parallel Circuits + - V C3C3 C1C1 C2C2 + - V C2C2 C1C1 C3C3 Parallel Series

16. Capacitors in Parallel Circuits The total charge stored on the capacitors in a parallel circuit is equal to the sum of the charges stored on all of the capacitors. Voltage is the same across all of the capacitors. q 1 = C 1 V; q 2 = C 2 V; q 3 = C 3 V q total = q 1 + q 2 + q 3 C eq = q/V = C 1 + C 2 + C 3… + - V C3C3 C1C1 C2C2 +q1+q1 -q1-q1 -q2-q2 -q3-q3 +q2+q2 +q3+q3

17. Capacitors in Series Circuits When capacitors are connected in series, the charge on them is the same irrespective of the capacitance. When capacitors are connected in series, the sum of the voltages for each capacitor equals the potential for the circuit. + - V C2C2 C1C1 C3C3 V3V3 V2V2 V1V1 +q+q -q-q +q+q +q+q -q-q -q-q

18. Capacitors in Series Circuits V 1 = q/C 1 ; V 2 = q/C 2 ; V 3 = q/C 3 Total voltage in a series circuit is equal to the sum of the voltages. Therefore: V = V 1 + V 2 + V 3 V = q/C 1 + q/C 2 + q/C 3 V = q (1/C 1 + 1/C 2 + 1/C 3 ) C eq = q/V 1/C eq = 1/C 1 + 1/C 2 + 1/C 3… V = q/C eq Solve for V

19. Energy Stored in a Capacitor A capacitor stores charge in the form of electrical energy. This is why capacitors have features of batteries. The amount of work required to fully charge a capacitor is equal to the final charge q multiplied by the average voltage as follows: W = ½ qV (V = ½ V) This work is also equal to the stored potential energy in the capacitor (U). Since q = CV, we can substitute this into 1 to obtain: U = ½CV 2 Similarly, since V = q/C: U = ½ q 2 /C

20. Key Ideas Capacitors store electrical energy. Capacitance is dependent on the geometry of the capacitor and not the voltage or charge. Capacitance is the ratio of the charge on one of the plates of the capacitor and the voltage. The plates in a capacitor are equally and oppositely charged. A dielectric media gives a capacitor a greater ability to carry charge. Current does not flow through capacitors under normal circumstances.