Physics 1161 PreLecture 11 RC Circuits Textbook Section

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

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. + e • 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 q • Intermediate – more complex q(t) = q (1 -e-t/RC) I(t) = I 0 e-t/RC + R - I + S 1 RC 2 RC q 0 t C S 2

RC Circuits: Discharging • Loop: q(t) / C + I(t) R = 0 • Just after…: q=q 0 + R – Capacitor is still fully charged – q 0 / C + I 0 R = 0 I 0 = -q 0 / (RC) e + - I - C • Long time after: Ic=0 – Capacitor is discharged (like a wire) S 1 – q / C = 0 q = 0 • Intermediate (more complex) q(t) = q 0 e-t/RC Ic(t) = I 0 e-t/RC + - RC S 2 2 RC q 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 Charging q(t) = q (1 -e-t/RC) V(t) = V (1 -e-t/RC) I(t) = I 0 e-t/RC Discharging q(t) = q 0 e-t/RC V(t) = V 0 e-t/RC I(t) = I 0 e-t/RC Time Constant t = RC Large t means long time to charge/discharge Short term: Charge doesn’t change (often zero or max) Long term: Current through capacitor is zero.