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Capacitance and Resistance

Capacitance and Resistance. Sandra Cruz-Pol, Ph. D. INEL 4151 Electromagnetics I ECE UPRM Mayagüez, PR. Resistance. If the cross section of a conductor is not uniform we need to integrate: Solve Laplace eq. to find V Then find E from its differential And substitute in the above equation.

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Capacitance and Resistance

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  1. Capacitance and Resistance Sandra Cruz-Pol, Ph. D. INEL 4151 Electromagnetics I ECE UPRM Mayagüez, PR

  2. Resistance • If the cross section of a conductor is not uniform we need to integrate: • Solve Laplace eq. to find V • Then find E from its differential • And substitute in the above equation

  3. Capacitance • Is defined as the ratio of the charge on one of the plates to the potential difference between the plates: • Assume Q and find V (Gauss or Coulomb) • Assume V and find Q (Laplace) • And substitute E in the equation.

  4. To find E, we will use: from Gauss’s Law From this we can get: • Poisson’s equation: • Laplace’s equation: (if charge-free)

  5. Relaxation Time • Recall that: • Multiplying, we obtain the Relaxation Time: • Solving for R, we obtain it in terms of C:

  6. P.E. 6.8 find Resistance of disk of radius b and central hole of radius a. Laplace’s equation: In cylindrical coordinates (if charge-free) =0 b a

  7. P.E. 6.8 find Resistance of disk of radius b and central hole of radius a. b a

  8. Capacitance • Parallel plate • Coaxial • Spherical

  9. Parallel plate Capacitor Plate area, S • Charge Q and -Q Dielectric, e

  10. Plate area, S - - - - - - Dielectric, e + + + - + + c - - Coaxial Capacitor • Charge +Q & -Q

  11. Spherical Capacitor • Charge +Q & -Q

  12. Capacitors connection • Series • Parallel Examples:

  13. In summary :

  14. Method of Images •  (or mirror charges) is a problem-solving tool in electrostatics.

  15. Method of Images •  Use superposition • Valid only for top region (where Q is)

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