1 / 16

Capacitance�and�Dielectrics

Capacitance�and�Dielectrics. Definition of Capacitance Calculating Capacitance Combinations of Capacitors Energy Stored in a Charged Capacitor Capacitors with Dielectrics. Definition of Capacitance.

josiah
Télécharger la présentation

Capacitance�and�Dielectrics

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Capacitance�and�Dielectrics Definition of Capacitance Calculating Capacitance Combinations of Capacitors Energy Stored in a Charged Capacitor Capacitors with Dielectrics

  2. Definition of Capacitance • Two  conductors  carrying  charges  of equal magnitude  but  of  opposite sign is a capacitor • The conductors are called plates • The capacitance C of a capacitor is the ratio of the magnitude of the charge on either conductor to the magnitude of the potential difference between  them: • The SI unit of capacitance is the farad (F)

  3. Calculating Capacitance • Parallel-Plate Capacitors • It consists of two parallel plates with area A separated by distance d • One plate carries a charge Q, and the other carries a charge Q • If A is large, then larger Q can be distributed over A (expectation : capacitance proportional to A) • If d is increased, the charge decreases (capacitance  to be  inversely proportional to ).

  4. Parallel-Plate Capacitors • Suppose the charge density is • Using Gauss’s law, the electric field is • Potential difference between the plates equals Ed • The capacitance

  5. Cylindrical Capacitors • The potential difference between A and B

  6. Spherical Capacitors • The potential difference • The capacitance

  7. Symbol

  8. COMBINATIONS OF CAPACITORS • Parallel Combination • the individual potential differences across capacitors connected in parallel are all  the  same and are equal to the potential difference applied across the combination. • The total charge Q stored by the two capacitors is • And • Thus

  9. Series Combination • The charges on capacitors connected in series are the same • The voltage across the battery  terminals is split between the two capacitors: • And • We get • Finally

  10. Example: Combining the capacitors

  11. Energy Stored in a Charged Capacitor • Suppose we charge the capacitor and q is charge at some instant during charging process. The potential difference is • To transfer an increment  of  chargedq, the work • Total work • Or

  12. Energy Density • Energy in capacitor • We may get • Thus energy per unit volume (energy density)

  13. CAPACITORS WITH DIELECTRICS • A dielectric is a non conducting material, such as rubber, glass, or waxed paper • When a dielectric is inserted between the plates of a capacitor, the capacitance increases • If  the dielectric completely fills  the  space between  the plates,  the capacitance  increases  by  a  dimensionless  factor  k�,  which  is  called  the  dielectric  constant • The voltages with and without the dielectric are related by the factor k as follows • Because the charge Q0 on the capacitor does not  change, we conclude that the capacitance must change to the value

  14. CAPACITORS WITH DIELECTRICS(2) A dielectric provides the following advantages: • Increase in capacitance • Increase in maximum operating voltage • Possible mechanical  support between  the plates, which  allows  the plates  to be close together without touching, thereby decreasing d and increasing C

  15. Dielectric Constants

More Related