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Agenda

Agenda. Today Finish Chapter 26: RC Circuits Freedom? Post-Freedom Magnetism & Induction: 27-29 Post-Post Freedom Finish induction & Review, Exam II. Capacitors in Circuits. Series 1/C T = 1/C 1 + 1/C 2 … Effective Distance increased, reduces C T Parallel C T = C1 + C2 + C3…

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Agenda

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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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