Physics 1161 Lecture 11RC Circuits

Time Constant Demo

• Which system will be brightest?• Which lights will stay on longest?• Which lights consume more energy?

2

Each circuit has a 0.5 F capacitor charged to 9 Volts.When the switch is closed:

1

= 2RC = RC/2

Time Constant Demo

• Which system will be brightest?• Which lights will stay on longest?• Which lights consume more energy?

2

Each circuit has a 0.5 F capacitor charged to 9 Volts.When the switch is closed:

1

= 2RC = RC/2

2 I=2V/R

1

Same U=1/2 CV2

Preflight 11.1, 11.3

2R

C R

S2

Both switches are initially open, and the capacitor is uncharged. What is the current through the battery just after switch S1 is closed?

1) Ib = 0

2) Ib = /(3R)

3) Ib = /(2R)

4) Ib = /R

S1

Ib

+

-

+

+

-

-

Both switches are initially open, and the capacitor is uncharged. What is the current through the battery after switch 1 has been closed a long time?

1) Ib = 0 2) Ib = V/(3R) 3) Ib = V/(2R) 4) Ib = V/R

15%

4%

62%

19%

50% 0% 35% 15%

Practice!

Calculate current immediately after switch is closed:

Calculate current after switch has been closed for 0.5 seconds:

Calculate current after switch has been closed for a long time:

Calculate charge on capacitor after switch has been closed for a long time:

R

CE

S1

R=10C=30 mF

E =20 Volts

-

Practice

Calculate current immediately after switch is closed:

Calculate current after switch has been closed for 0.5 seconds:

Calculate current after switch has been closed for a long time:

Calculate charge on capacitor after switch has been closed for a long time:

R

CE

S1

R=10C=30 mF

E =20 Volts

- I0R - q0/C = 0I

+

+

+

-

-

- - I0R - 0 = 0

I0 = /R

After a long time current through capacitor is zero!

- IR - q∞/C = 0

+ 0 - q∞ /C = 0q∞ = C

0

t

RCI I e

0.5

RCeR

0.5

10 0.0320

10e

0.5

10 0.0320

10e

0.38 A

Both switches are closed. What is the final charge on the capacitor after the switches have been closed a long time?

1 2 3 4

25% 25%25%25%

IR

S2S1

+- R

+

-

C

2R+ -1. Q = 02. Q = C /33. Q = C /24. Q = C

Charging: Intermediate Times

Calculate the charge on the capacitor 310-3 seconds after switch 1 is closed.

q(t) = q(1-e-t/RC)

C R1

S2

S1

Ib

+

-

+

+

-

-

R1 = 20

R2 = 40

ε = 50 Volts

C = 100FR2

Charging: Intermediate Times

C R1

S2

S1

Ib

+

-

+

+

-

-

Calculate the charge on the capacitor 310-3 seconds after switch 1 is closed.

q(t) = q(1-e-t/R2C)

= q(1-e-310-3 /(4010010-6)))

= q (0.53)

Recall q = ε C

= (50)(100x10-6) (0.53)

= 2.7 x10-3 Coulombs

R1 = 20

R2 = 40

ε = 50 Volts

C = 100FR2

RC Circuits: Discharging

• KLR: ____________

• Just after…: ________– Capacitor is still fully charged

• Long time after: ____________

• Intermediate (more complex)– q(t) = q0 e-t/RC

– Ic(t) = I0 e-t/RC

C

R

S1

+

+

I-

-

S2

q

RC 2RC

t

RC Circuits: Discharging

• KLR: 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– q / C = 0 q = 0

• Intermediate (more complex)– q(t) = q0 e-t/RC

– Ic(t) = I0 e-t/RC

C

R

S1

+

+

I-

-

S2

q

RC 2RC

t

Preflight 11.5After switch 1 has been closed for a long time, it is opened and switch 2 is closed. What is the current through the right resistor just after switch 2 is closed?

1) IR = 0

2) IR = /(3R)

3) IR = /(2R)

4) IR = /R

KLR: -q0/C+IR = 0

Recall q is charge on capacitor after charging:q0= C (since charged w/ switch 2 open!)- + IR = 0 I = /R

2R

C R

S2S1

IR

+

-

+

+

-

-

+

-

27%

27%

4%

42%

After being closed for a long time, the switch is opened. What is the charge Q on the capacitor 0.06 seconds after the switch is opened?

E = 24 Volts

R = 4

C = 15 mF

RC

2R

E

S1

1. 0.368 q0

2. 0.632 q0

3. 0.135 q0

4. 0.865 q0

After being closed for a long time, the switch is opened. What is the charge Q on the capacitor 0.06 seconds after the switch is opened?

1 2 3 4

25% 25%25%25%

E = 24 Volts

R = 4

C = 15 mF

RC

2R

E

S1

q(t) = q0 e-t/RC

= q0 (e-0.06 /(4(1510-3)))

= q0 (0.368)

1. 0.368 q0

2. 0.632 q0

3. 0.135 q0

4. 0.865 q0