1. Today’s Concept: RC Circuits
Physics 2112 Unit 11
Today’s Concept:
RC Circuits

2. RC Circuit (Charging) Kirchoff’s Voltage Rule Differential Equation
Capacitor uncharged, Switch is moved to position “a” a R
Vbattery C b R
Vbattery C a b
Kirchoff’s Voltage Rule
Differential Equation
Draw switch being closed
Draw current at t = 0
Draw VC = 0
Reveal short term equation
After long term, indicate IC = 0 implies VR = 0
Unit 11, Slide 2

3. Example 11.1 (Charging Capacitor)
C1 = 1uF
R1 = 1.2MW
10V
What is the charge on the capacitor 1second after the switch is closed? What is the current through the resistor 1 second after the switch is closed?
Conceptual Idea:
Use charging equations for a capacitor.
Note:
e-1 = 0.37
1-e-1 = 0.63
Plan:
Find time constant, t
Find Qf and Io
Put in t=1sec

4. Example 11.2 (Charging Capacitor)
C1 = 1uF
R1 = 1.2MW
10V
What is the charge on the capacitor 10 seconds after the switch is closed? What is the current through the resistor 10 seconds after the switch is closed?
Conceptual Idea:
Use charging equations for a capactor.
Plan:
Find time constant, t
Find Qf and Io
Put in t=1sec

5. RC Circuit (Discharging)
Capacitor has q0 = CV, Switch is moved to position “b”
Kirchoff’s Voltage Rule R
Vbattery C a b R
Vbattery C a b I + -
Differential Equation
Counterclockwise current V -I
Unit 11, Slide 5

6. Example 11.3 (Discharging Capacitor)
C1 = 1uF
R1 = 1.2MW
10V 1
The switch is held in position 1 for a long time and the capacitor becomes fully charged. It is then flipped to position 2. What is the charge on the capacitor 2 seconds after the switch is flipped? 2
Conceptual Idea:
Use discharging equations for a capacitor.
Plan:
Find time constant, t
Find Qo
Put in t=2sec

7. How do Exponentials Work?
“Fraction of initial
charge that remains”
Not all curves that
look like
are exponential!!
“How many time constants worth
of time that have elapsed”
Unit 11, Slide 7

8. the longer it takes to get the same change…
RC = 2
Time constant:
t = RC
The bigger t is,
the longer it takes to get the same change…
RC = 1
Unit 11, Slide 8