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Understanding Capacitors in Circuits: A Guide to RC Circuits and Induction

Explore the fundamentals of RC circuits, the impact of capacitors in parallel and series configurations, voltage and current dependencies, and the behavior of capacitors over time. Delve into the principles of magnetism and induction, followed by a review for Exam II. Discover the significance of discharge circuits and examine boundary values for capacitor discharging processes. Gain insights into the behavior of capacitors, resistors, and lamps within circuits as they interact with time constants and discharge processes.

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Understanding Capacitors in Circuits: A Guide to RC Circuits and Induction

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  1. Agenda • Today • Finish Chapter 26: RC Circuits • Freedom? • Post-Freedom • Magnetism & Induction: 27-29 • Post-Post Freedom • Finish induction & Review, Exam II

  2. Capacitors in Circuits • Series • 1/CT = 1/C1 + 1/C2 … • Effective Distance increased, reduces CT • Parallel • CT = C1 + C2 + C3… • Effective Area increased, increases CT • Effectively opposite of Resistors • What is voltage dependence for R’s? • Current • What is voltage dependence for C’S? • Charge • I = dQ/dt ….

  3. What Happens Here? Start with Switch Open? Close Switch Lamp + -

  4. What Happens Here? Start with Switch Open? Close Switch What occurs now? Changes with Time? At t=0, cap’s are shorts Filling with charge, no opposition to flow At t= infinity, cap’s are opens Filled with charge After a long time…. Lamp + -

  5. What Happens Here? Start with Switch Open? Close Switch What occurs now? Changes with Time? At t=0, cap’s are shorts Filling with charge, no opposition to flow At t= infinity, cap’s are opens Filled with charge After a long time…. Voltage on Capacitor = Voltage of Cell No current flow, Lamp is off Now take out battery, replace with switch Lamp + + - -

  6. What Happens Here? What Happens when switch is closed? Path emerges for charge to flow Light back on for some time Dims, then off as charge dissipates Lamp + -

  7. Discharge Circuit Capacitor Begins with Voltage V Q=VC Lamp = Resistor value R Assume constant R for simplicity Define states: Initial & Final Initial (t=0) switch JUST closed Final (t=infinity) looong time after Initial, Current max or min? Max Final, Current max or min? Min (zero) Now we have “boundary values” Next up: DiffEQ Lamp + -

  8. Discharge Circuit Q=VC Initial: VC = V, I=I0 Final: VC = 0, I = 0 Examine Voltage Loop VC + IR = 0 R Lamp resistance Holds true for any time Q/C = -IR Q/C = -R(dQ/dt) -(Q/C)dt = RdQ -dt/(RC) = dQ/Q Integrate Both Sides (tau) = RC [Time Constant] Lamp + -

  9. Discharge Circuit Q=VC Initial: VC = V, I=I0, q = Q0 Final: VC = 0, I = 0, q = 0 -dt/(RC) = dQ/Q Integrate Both Sides (tau) = RC [Time Constant] Lamp + - Book does same by choosing integration limits Here: Use constants to match boundary conditions

  10. Discharge Circuit Q=VC Initial: VC = V, I=I0, q = Q0 Final: VC = 0, I = 0, q = 0 -dt/(RC) = dQ/Q Integrate Both Sides (tau) = RC [Time Constant] Lamp + - What should A be?

  11. Discharge Circuit Q=VC Initial: VC = V, I=I0, q = Q0 Final: VC = 0, I = 0, q = 0 -dt/(RC) = dQ/Q Integrate Both Sides (tau) = RC [Time Constant] Lamp + - Charge not usually too useful Voltage?

  12. Discharge Circuit Q=VC Initial: VC = V, I=I0, q = Q0 Final: VC = 0, I = 0, q = 0 -dt/(RC) = dQ/Q Integrate Both Sides (tau) = RC [Time Constant] Lamp + - Charge not usually too useful Voltage?

  13. Discharge Circuit Q=VC Initial: VC = V, I=I0, q = Q0 Final: VC = 0, I = 0, q = 0 -dt/(RC) = dQ/Q Integrate Both Sides (tau) = RC [Time Constant] Lamp + - Charge not usually too useful Current?

  14. Charge Circuit? Lamp Pretty Similar… + -

  15. Problems? Freedom? • Today • Finish Chapter 26: RC Circuits • Freedom? • Post-Freedom • Magnetism & Induction: 27-29 • Post-Post Freedom • Finish induction & Review, Exam II

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