RC Circuits

1
RC Circuits
Physics 1161 Pre-Lecture 11

• Textbook Section 21-6 21-7

2
Combine RC 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
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 Circuits Discharging

• Loop q(t) / C I(t) R 0
• Just after qq0
• Capacitor is still fully charged
• q0 / C I0 R 0 ? I0 -q0 / (RC)
• Long time after Ic0
• 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 doesnt change (often zero or
max) Long term Current through capacitor is zero.