RC Circuits Textbook Section 21-6 & 21-7 Physics 1161: Pre-Lecture 11

Combine R+C Circuits Gives time dependence –Current is not constant I(t) –Charge is not constant q(t) Used for timing –Pacemaker –Intermittent windshield wipers Models of nervous system include R, C

RC Circuits Charging The switches are originally opened and the capacitor is uncharged. Then, switch S 1 is closed. Just after S 1 is closed, q on the capacitor is 0, V across capacitor is 0, and I is maximum: I =  /R Long time after, capacitor is fully charged: Q =  C; I = 0; V across capacitor is  Intermediate – more complex q(t) = q  (1-e -t/RC ) I(t) = I 0 e -t/RC S2S2 I  + - C R S1S1 t q RC 2RC 0 qq

RC Circuits: Discharging Loop: q(t) / C + I(t) R = 0 Just after…: q=q 0 –Capacitor is still fully charged –q 0 / C + I 0 R = 0  I 0 = -q 0 / (RC) Long time after: I c =0 –Capacitor is discharged (like a wire) –q  / C = 0  q  = 0 Intermediate (more complex) q(t) = q 0 e -t/RC I c (t) = I 0 e -t/RC C  R S1S I S2S2 q RC2RC t

Capacitor “Rules of Thumb” Initially uncharged capacitor: –acts like a wire (short circuit) at t = 0 –acts like an open circuit (broken wire) as t   Initially charged capacitor: –acts like a battery at t = 0

RC Summary ChargingDischarging 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 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