Class 37: Charging and Discharging RL Circuits Course Evaluation: 1. - - PowerPoint PPT Presentation

Class 37: Charging and Discharging RL Circuits

Course Evaluation:

• 1. Starts Wednesday, ends Dec 10th.
• 2. Go to http://pa.as.uky.edu/
• 3. Click at “UNDERGRADUATES” in the top menu and then choose the

first item: Physics & Astronomy Course Evaluations

• 4. Follow instructions from there.
• 5. Make sure remember or write down any given key or password. You

need this to re-enter the system if you cannot finish the evaluation in

• ne time.

RC Circuits – Charging

 C R

) e 1 ( C q C

• K

K C q 0, At t e K C q ) e (K Ke C

• q

K' CR t

• )

C

• q

n( dt CR 1

• C
• q

dq dt q)

• (C

dq CR t d q d R C q IR C q

CR t

• CR

t

• K'

CR t

• 

                                      ) e

• (1

C q V e IR V e R e CR C t d dq I

CR t

• C

CR t

• R

CR t

• CR

t

• 

           

Integration constant VR + VC = 

From Class 22 Slide #3 Charge

RL Circuits – Charging

) e 1 ( R I ) e 1 ( R I K K I 0, At t Ke IR ) e (K Ke IR

• K'

L R t L R ) IR

• n(

K' t ) IR

• n(

R L dt IR

• dI

L IR)dt

• (

dI L dt dt R I dI L IR t d I d L

t L R

• t

L R

• t

L R

• K'

L R t L R

• 

                                              

t L R

• e

dt dI L V ) e 1 ( IR V

L t L R

• R

        

Integration constant VR + VC = 

Current

 L R

RC time constant

=RC is known as the RC time constant. It indicates the response time (how fast you can charge up the capacitor) of the RC circuit.

e R I

CR t

• 

 R I  

t

R 37 . ~ R e I

1

• 

 

t=RC

) e 1 ( C q

CR t

• 

   C q 

t

  C 63 . ~ C ) e 1 ( q

• 1

 

t=RC

37 . e 2.72 e

1

• 

 707 . 2 1 1.414 2  

Nothing to do with RC circuits From Class 23 Slide #4

L/R time constant

=L/R is known as the time constant. It indicates the response time (how fast you can up a current) of the RC circuit.

e L t d I d

t L R

• 

 L dt dI  

t

L 37 . ~ L e dt dI

1

• 

 

t=L/R

) e 1 ( R I

t L R

• 

  R I  

t

R 63 . ~ R ) e 1 ( I

1

• 

  

t=L/R

37 . e 2.72 e

1

• 

 707 . 2 1 1.414 2  

Nothing to do with RL circuits

RC Circuits – Discharging

CR t

• CR

t

• K'

CR t

• Qe

q K Q Q q 0, At t e K q ) e (K Ke q K' CR t

• q

n dt CR 1

• q

dq dt q

• dq

CR t d q d R C q IR C q                        

CR t

• C

CR t

• R

CR t

• e

C Q C q V e C Q IR V e RC Q t d dq I          

Integration constant VR + VC = 0

C R

Charge From Class 23 Slide #5

RL Circuits – Discharging

e R

• r

e I I R I K R I I 0, At t ) e (K Ke I K' t L R

• I

n dt L R

• I

dI

• IRdt

LdI IR dt dI L

t L R

• t

L R

• K'

t L R

• 

                      

t L R

• L

t L R

• R

CR t

• Re

I

• t

d I d L V Re I IR V e I I       

Integration constant VR + VL = 0

Current

 L R

Note special switch

charge discharge

In Summary

For both charge and discharge, Q, I, VC, and VR must be one of the following two cases:

t t

RC t

• 0e

y y 

y can be Q, I, VC, or VR y y0 y y

) e

• (1

y y

RC t

• 



From Class 23 Slide #7

In Summary

For both charge and discharge, I, dI/dt, VL, and VR must be one of the following two cases:

t t

RC t

• 0e

y y 

y can be I, dI/dt, VL, or VR y y0 y y

) e

• (1

y y

RC t

• 

