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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.

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Capacitance�and�Dielectrics

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  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

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