Lect07 handout

RC Circuits Physics 102: Lecture 7

Recall …. ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

RC Circuits ,[object Object],[object Object],[object Object],[object Object]

RC Circuits ,[object Object],[object Object],R K C S + + + R Na R Cl ε K ε Na ε Cl

Capacitors ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Charging Capacitors ,[object Object],[object Object], R C S

Charging Capacitors: t=0 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object], R C S R 

Charging Capacitors: t>0 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object], R C + - Demo R 

ACT/Preflight 7.1 ,[object Object],2R C  R S 2 1) I b = 0 2) I b = E /(3R) 3) I b = E /(2R) 4) I b = E /R S 1 I b + - + + - -

ACT/Preflight 7.3 ,[object Object],1) I b = 0 2) I b = E /(3R) 3) I b = E /(2R) 4) I b = E /R 2R C  R S 2 S 1 I b + - + + - -

Discharging Capacitors ,[object Object],[object Object],R C S

Discharging Capacitors ,[object Object],[object Object],[object Object],[object Object],[object Object],R C + - Demo

ACT/Preflight 7.5 ,[object Object],1) I R = 0 2) I R =  /(3R) 3) I R =  /(2R) 4) I R =  /R 2R C  R S 2 S 1 I R + - + + - - + -

ACT: RC Circuits ,[object Object],1) Q = 0 2) Q = C E /3 3) Q = C E /2 4) Q = C E R 2R C  S 2 S 1 I R + - + + - - + -

RC Circuits: Charging ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],C  R S 1 S 2 + + + I - - - The switches are originally open and the capacitor is uncharged. Then switch S 1 is closed. t q RC 2RC 0 q 

RC Circuits: Discharging ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],C  R S 1 - + + I - + - S 2 q RC 2RC t

What is the time constant? ,[object Object],[object Object],[object Object]

Time Constant Demo ,[object Object],[object Object],[object Object],Each circuit has a 1 F capacitor charged to 100 Volts. When the switch is closed: 1 Example 2

Summary of Concepts ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Practice! Calculate current immediately after switch is closed: Calculate current after switch has been closed for 0.5 seconds: Calculate current after switch has been closed for a long time: Calculate charge on capacitor after switch has been closed for a long time: Example E – I 0 R – q 0 /C = 0 + + + - - - E – I 0 R – 0 = 0 I 0 = E /R After a long time current through capacitor is zero! E – IR – q ∞ /C = 0 E – 0 – q ∞ /C = 0 q ∞ = E C R C ε S 1 R=10  C=30 mF ε =20 Volts I

ACT: RC Challenge ,[object Object],1) 0.368 q 0 2) 0.632 q 0 3) 0.135 q 0 4) 0.865 q 0 R C ε 2R S 1 ε = 24 Volts R = 2  C = 15 mF

Charging: Intermediate Times  Calculate the charge on the capacitor 3  10 -3 seconds after switch 1 is closed. ,[object Object],= q  (1-e - 3  10 -3 /(20  100  10 -6) ) ) = q  (0.78) Recall q  =  C = (50)(100x10 -6 ) (0.78) = 3.9 x10 -3 Coulombs R = 10  V = 50 Volts C = 100  F Example 2R C R S 2 S 1 I b + - + + - -

RC Summary Charging Discharging q(t) = q  (1-e -t/RC ) q(t) = q 0 e -t/RC V(t) = V  (1-e -t/RC ) V(t) = V 0 e -t/RC I(t) = I 0 e -t/RC I(t) = I 0 e -t/RC Short term: Charge doesn’t change (often zero or max) Long term: Current through capacitor is zero. Time Constant  = RC Large  means long time to charge/discharge

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