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RC Circuits

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. +. R. +. e.

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RC Circuits

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

  2. 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

  3. + R + e - I - C + - S2 S1 RC 2RC q q 0 t RC Circuits Charging • The switches are originally opened and the capacitor is uncharged. Then, switch S1 is closed. • Just after S1 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) = I0e-t/RC

  4. RC 2RC q t RC Circuits: Discharging + • Loop: q(t) / C + I(t) R = 0 • Just after…: q=q0 • Capacitor is still fully charged • q0 / C + I0 R = 0  I0 = -q0 / (RC) • Long time after: Ic=0 • Capacitor is discharged (like a wire) • q / C = 0  q = 0 • Intermediate (more complex) q(t) = q0 e-t/RC Ic(t) = I0 e-t/RC R + e - I - C + - S1 S2

  5. 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

  6. RC Summary Charging Discharging q(t) = q(1-e-t/RC) q(t) = q0e-t/RC V(t) = V(1-e-t/RC) V(t) = V0e-t/RC I(t) = I0e-t/RC I(t) = I0e-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.

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