Lecture_11-1 - Lecture 11 1/18 Capacitor in RC Circuits I I...

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Lecture 11 1/18 I charging I discharging Switch closed at t=0 Initial Capacitor (C) initially uncharged V 0 = 0 across C I 0 = Emf/R Final (after a long time) Capacitor (C) fully charged V = Emf across C I = 0 Capacitor in RC Circuits Switch closed at t=0 Initial Capacitor (C) initially charged V 0 = Q 0 /C across C I 0 = V 0 /R Final (after a long time) Capacitor (C) fully discharged V = 0 across C I = 0
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Lecture 11 2/18 Discharging a Capacitor in RC Circuits I 1. Switch closed at t=0. Initially C is fully charged with Q 0 2. Loop Rule: 3. Convert to a differential equation 4. Solve it! 0 R I C Q 0 dt dQ R C Q dt dQ I C R t Q Q C R dt Q dQ 0 ln C R t C R t e C R Q dt dQ I e Q Q 0 0 RC is the time constant ( τ )
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Lecture 11 3/18 Charge Q(t) during Discharging Charge on the capacitor as a function of time: Q 0 is the initial charge 0.37 Q 0 time constant / 0 / 0 ) ( t C R t e Q e Q t Q s A C V C C R ] [ ] [ 0 1 0 37 . 0 ) ( Q e Q Q Charge after time τ is given by: units of the time constant ( τ ) are seconds
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Lecture 11 4/18 Current I(t) during Discharging Current from the capacitor as a function of time: I 0 is the initial current / 0 ) ( t e Q t Q 0 1 0 37 . 0 ) ( I e I I Charge after time τ is given by: / 0 ) ( t e I t I / 0 / 0 t t e I e Q I dt dQ I Starting with R V C R Q Q I 0 0 0 0
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Lecture 11 5/18 Charging a Capacitor in RC Circuits 1. Switch closed at t=0.
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