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Understanding Kirchhoff’s Methods for Resistors and Capacitors in RC Circuits

Explore the clever methods of applying Kirchhoff's laws to find voltages and currents in resistive circuits. Learn how to define currents, utilize node and loop laws to simplify variables, and derive necessary equations for solving complex circuits. The content also covers the combination of capacitors in both series and parallel connections, highlighting the differences in voltage and charge across these configurations. With step-by-step examples of charging and discharging behaviors in RC circuits, you'll gain a deeper understanding of critical electrical concepts.

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Understanding Kirchhoff’s Methods for Resistors and Capacitors in RC Circuits

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  1. Another Resister example: find all the voltages and currents… Clever hippie way Kirchhoff’s method

  2. Another Resister example: find all the voltages and currents… Clever hippie way

  3. Another Resister example: find all the voltages and currents… b) Now try Kirchhoff's method The procedure …

  4. Another Resister example: find all the voltages and currents… 1.) Define currents

  5. Another Resister example: find all the voltages and currents… 2.) use node law to reduce variables

  6. Another Resister example: find all the voltages and currents… 3.) use loop laws to get equations Solve em ….

  7. Another Resister example: find all the voltages and currents… 4.) Solve em.

  8. Recall Capacitors?

  9. Capacitors in circuits (DC)

  10. Equivalent Capacitors: Parallel connection

  11. Equivalent Capacitance?

  12. Parallel capacitors Same voltage!

  13. Equivalent Capacitors: Series connection.

  14. Equivalent Capacitance ? External charge stored

  15. Equivalent Capacitance ?

  16. Series capacitors Same charge!

  17. NOTE: The Rules for combining series and parallel capacitors are BACKWARDS from The Rules for combining series and parallel resistors !

  18. Number example ( all C = 10 mF)

  19. Parallel EXAMPLE

  20. Series EXAMPLE Next page room

  21. RC Circuits – time behavior!

  22. t = 0, switch just closed CHARGING

  23. t1: Now some time has passed CHARGING

  24. t2: Now a lot of time has passed CHARGING

  25. CHARGING

  26. CHARGING

  27. CHARGING Number example: What are the voltages across R and across C at a time t = 0.010 s after the switch is closed? Next page

  28. DISCHARGING RC Circuits – time behavior!

  29. DISCHARGING RC Circuits – time behavior!

  30. DISCHARGING

  31. DISCHARGING

  32. DISCHARGING Number example: What are the voltages across R and across C at a time t = 0.010 s after the switch is closed? Next page

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