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Physics 2112 Unit 11 Today’s Concept: RC Circuits Unit 11, Slide 1
Physics 2112Unit 11
Today’s Concept:RC Circuits
Unit 11, Slide 1
RC Circuit (Charging)
Kirchoff’s Voltage Rule
RVbattery
Ca
b
a
RVbattery
C
b
Capacitor uncharged, Switch is moved to position “a”
0 IRCqVbattery
0 Rdtdq
CqVbattery
RCteCVtq /1)( RCteItI /0)(
Unit 11, Slide 2
)(1 VCqRCdt
dqRCq
RVbat
Differential Equation
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?C1 = 1uF
R1 = 1.2MW
10V
Example 11.1 (Charging Capacitor)
Conceptual Idea:
Use charging equations for a capacitor.
Plan:• Find time constant, t• Find Qf and Io• Put in t=1sec
Note: • e-1 = 0.37
• 1-e-1 = 0.63
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?C1 = 1uF
R1 = 1.2MW
10V
Example 11.2 (Charging Capacitor)
Conceptual Idea:
Use charging equations for a capactor.
Plan:• Find time constant, t• Find Qf and Io• Put in t=1sec
Kirchoff’s Voltage Rule
RC Circuit (Discharging)
RVbattery
Ca
b
V
Capacitor has q0 CV, Switch is moved to position “b”
RVbattery
Ca
bI+
I
0++ IRCq
0++ Rdtdq
Cq
RCteqtq /0)( RCteItI /
0)(
Unit 11, Slide 5
Differential Equation
Qdq
RCdt
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?C1 = 1uF
R1 = 1.2MW
10V
Example 11.3 (Discharging Capacitor)
Conceptual Idea: Use discharging equations for a capacitor.
Plan:• Find time constant, t• Find Qo • Put in t=2sec
1
2
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 1 2 3 4 5 6 7 8 9 10
“Fraction of initial charge that remains”
“How many time constants worth of time that have elapsed”
How do Exponentials Work?
RCt
eQtQ 0)(
0
)(Q
tQ
RCt
Unit 11, Slide 7
Not all curves that look like are exponential!!
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 1 2 3 4 5 6 7 8 9 10
RC 1
RC 2
Time constant:t RC
The bigger t is,the longer it takes to getthe same change…
0
)(Q
tQRCteQtQ 0)(
tUnit 11, Slide 8
