rc circuits - Charging a capacitor Capacitors do not...

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1 1 RC Circuits Circuits with resistors and capacitors Today Recently Circuits with resistors This lecture: HRW 27.9 For next time: HRW 3.8,28.1-28.5 2 Charging a capacitor Capacitors do not conduct, because charge can’t flow across the gap. + + - - R C E If the switch has never been closed, there is no charge on the capacitor. Current flows until the capacitor is charged (or discharged) to its equilibrium value for that circuit. When the switch is closed, charge flows onto the plates. There are currents in RC circuits, and the currents vary with time. R C E -- ++ 3 Kirchhoff analysis of an RC circuit Kirchhoff’s laws apply to RC circuits. Recall, V=q/C for a capacitor, and the side with positive charge is at a higher potential. Also recall that: q = t d i. qq -R - =0 tC E So, , a differential equation. Suppose a switch in the circuit is closed at t=0. ⎛⎞ ⎜⎟ ⎝⎠ t RC q(t) =C 1-e E - Then, q=0 at t=0. The solution that satisfies this condition is: see the text for a way to derive this result i q - =0 C E loop law: R C E 4 t R R C t C - q(t) - q C =e t =1 - e RC C E E Charging a Capacitor It is straightforward to verify the solution: Substituting these into the differential equation, q t q - C E E E E t RC t RC - C 1 -
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rc circuits - Charging a capacitor Capacitors do not...

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