Capacitance and Resistance

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Presentation transcript:

Capacitance and Resistance Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I Capacitance and Resistance Sandra Cruz-Pol, Ph. D. INEL 4151 Electromagnetics I ECE UPRM Mayagüez, PR Electrical Engineering, UPRM (please print on BOTH sides of paper)

Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I 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 Electrical Engineering, UPRM (please print on BOTH sides of paper)

Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I 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. Electrical Engineering, UPRM (please print on BOTH sides of paper)

Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I To find E, we will use: from Gauss’s Law From this we can get: Poisson’s equation: Laplace’s equation: (if charge-free) Electrical Engineering, UPRM (please print on BOTH sides of paper)

Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I Relaxation Time Recall that: Multiplying, we obtain the Relaxation Time: Solving for R, we obtain it in terms of C: Electrical Engineering, UPRM (please print on BOTH sides of paper)

Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I 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 Electrical Engineering, UPRM (please print on BOTH sides of paper)

Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I P.E. 6.8 find Resistance of disk of radius b and central hole of radius a. b a Electrical Engineering, UPRM (please print on BOTH sides of paper)

Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I Capacitance Parallel plate Coaxial Spherical Electrical Engineering, UPRM (please print on BOTH sides of paper)

Parallel plate Capacitor Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I Parallel plate Capacitor Charge Q and -Q Plate area, S Dielectric, e Electrical Engineering, UPRM (please print on BOTH sides of paper)

Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I Dielectric, e Plate area, S + - c Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I Coaxial Capacitor Charge +Q & -Q Electrical Engineering, UPRM (please print on BOTH sides of paper)

Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I Spherical Capacitor Charge +Q & -Q Electrical Engineering, UPRM (please print on BOTH sides of paper)

Capacitors connection Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I Capacitors connection Series Parallel Examples: Electrical Engineering, UPRM (please print on BOTH sides of paper)

Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I In summary : C R Parallel Plate Coaxial Spherical Electrical Engineering, UPRM (please print on BOTH sides of paper)

Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I Method of Images (or mirror charges) is a problem-solving tool in electrostatics. Electrical Engineering, UPRM (please print on BOTH sides of paper)

Dr. S. Cruz-Pol, INEL 4151-Electromagnetics I Method of Images Use superposition Valid only for top region (where Q is) Electrical Engineering, UPRM (please print on BOTH sides of paper)