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Lecture 17: FRI 20 FEB 08

Physics 2102 Jonathan Dowling. Lecture 17: FRI 20 FEB 08. RC circuits Ch27.9. i (t). C E. E /R. RC Circuits: Charging a Capacitor. In these circuits, current will change for a while, and then stay constant. We want to solve for current as a function of time i(t)=dq/dt.

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Lecture 17: FRI 20 FEB 08

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  1. Physics 2102 Jonathan Dowling Lecture 17: FRI 20 FEB 08 RC circuits Ch27.9

  2. i(t) CE E/R RC Circuits: Charging a Capacitor In these circuits, current will change for a while, and then stay constant. We want to solve for current as a function of time i(t)=dq/dt. The charge on the capacitor will also be a function of time: q(t). The voltage across the resistor and the capacitor also change with time. To charge the capacitor, close the switch on a. VC=Q/C VR=iR A differential equation for q(t)! The solution is: Time constant: =RC

  3. Solution: i(t) + C E/R - RC Circuits: Discharging a Capacitor Assume the switch has been closed on a for a long time: the capacitor will be charged with Q=CE. +++ --- Then, close the switch on b: charges find their way across the circuit, establishing a current.

  4. Example The three circuits below are connected to the same ideal battery with emf E. All resistors have resistance R, and all capacitors have capacitance C. • Which capacitor takes the longest in getting charged? • Which capacitor ends up with the largest charge? • What’s the final current delivered by each battery? • What happens when we disconnect the battery? Compile R’s into into Req. Then apply charging formula with ReqC = 

  5. Example In the figure, E = 1 kV, C = 10 µF, R1 = R2 = R3 = 1 MW. With C completely uncharged, switch S is suddenly closed (at t = 0). • What’s the current through each resistor at t=0? • What’s the current through each resistor after a long time? • How long is a long time? Compile R1, R2, and R3 into Req. Then apply discharging formula with ReqC = 

  6. Shunt? What Shunt?

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