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Fundamentals of Electric Circuits: Capacitors and Inductors

Learn about the basics of electric circuits, including the functioning of capacitors and inductors. Understand how capacitors store electrical charge and energy, and how inductors produce magnetic fields. Solve differential equations to find transient responses and explore the dynamics of these components.

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Fundamentals of Electric Circuits: Capacitors and Inductors

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  1. Quiz 10 min

  2. Objectives • Continue with Fundamentals of Electric Circuits • Capacitors • Inductors

  3. Capacitors Consists of two conductive plates separated by a dielectric layer.

  4. Dynamic System t (or ) is time

  5. Current and voltage in the system with the capacitor

  6. Purpose of capacitors • store electrical charge or energy • generate huge voltages in the circuits

  7. Capacitors in Series and Parallel

  8. Example Find i as a function of C , R and VB

  9. Solving Differential Equation The transient response is the time required for the capacitor to fully charge, and is equivalent to about 5 time constants or 5T. 5T

  10. Solution based on intuition

  11. Magnetic Field Produced by Current An electric current in a wire produces a magnetic field around the wire that is proportional to the magnitude of the current The direction of the field follows the “right hand rule” put your thumb in the direction of the current, and your fingers wrap in the direction of the magnetic field

  12. Electromagnet If we have a coil of wire with a current through the wire, each turn will contribute to the magnetic field and we can produce an electromagnet The magneto-motive force (mmf) is the product of the current, I, and the number of turns, N; mmf = NI

  13. Inductors An inductor is constructed by coiling a wire around some type of form

  14. Dynamics system v − irelationship for inductance

  15. Inductor acts as a short circuit for DC

  16. We need a resistor

  17. Solving the Differential Equation 5T time required for the inductor to get full current is equivalent to about 5 time constants or 5T.

  18. Summary

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