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