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Capacitance

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

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Capacitance

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  1. Capacitance

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

  3. E- E+ - - - - - - - - - - - E- E+ + + + + + + + + + E- E+ 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 A EA = ½ E+ + -½ E- = 0 B EB = ½ E+ + ½ E- = E C EC = -½ E+ + ½ E- = 0

  4. - - - - - - - - - - - E + + + + + + + + + Electric Field of a Parallel Plate Capacitor • From Gauss’ Law: E = q/εoA where: εo = permittivity of free space = 8.854 x 10-12 C2/Nm2 A = Area of the plate

  5. - - - - - - - - - - - E + + + + + + + + + Electric Field of a Parallel Plate Capacitor • Since: E = ΔV/d And E = q/εoA • Set them equal to each other and rearrange to get: C = The ratio of charge per volt for any capacitor is call its capacitance 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=1915http://www.absorblearning.com/media/attachment.action?quick=qq&att=1915

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

  10. The Dielectric Constant • A dielectric is an insulating material that contains permanent dipole moments. Where: Eo= Electric field without a dielectric medium. E = Electric field with dielectric. • Eo > 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. Leads to q – qo CoV κ + 1 = Storing Electric Charge on a Parallel Plate Capacitor q = 2.6x10-5C • When a 1.2F capacitor has a slab of dielectric material, 2.6x10-5C of additional charge flows onto the plates. What is the dielectric constant? qo = CoV q = κCoV The extra charge equals Δq = q – qo q – qo = κCoV – CoV + + + + + + + + + + + ++++ - - - - - - - - - - - ---- C = 1.2F 2.8 • Note that the excess charge that the capacitor can store is exactly equal to the charge without the dielectric times the dielectric constant. + V = 12V

  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… • increase? • decrease? • 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. + V - C3 C1 C2 C1 + V - C2 C3 Capacitors in Series and Parallel Circuits Parallel Series

  16. +q2 +q1 +q3 + V - C3 C1 C2 -q1 -q3 -q2 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. q1 = C1V; q2 = C2V; q3 = C3V qtotal = q1 + q2 + q3 Ceq = q/V = C1 + C2 + C3…

  17. V1 C1 +q -q +q + V V2 - -q C2 -q +q C3 V3 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.

  18. Solve for V Capacitors in Series Circuits V1 = q/C1; V2 = q/C2; V3 = q/C3 Total voltage in a series circuit is equal to the sum of the voltages. Therefore: V = V1 + V2 + V3 V = q/C1 + q/C2 + q/C3 V = q (1/C1 + 1/C2 + 1/C3) Ceq = q/V 1/Ceq = 1/C1 + 1/C2 + 1/C3… V = q/Ceq

  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 = ½CV2 Similarly, since V = q/C: U = ½ q2/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.

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