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 10 th . 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 one time.

From Class 22 RC Circuits – Charging Charge Slide #3 q q d q        IR R C C d t C    CR dq (C - q) dt dq 1   Integration constant - dt  q - C CR t      n( q - C ) - K'  CR R t -     K' q - C Ke CR (K e ) t -     q C K e CR          At t 0, q 0 0 C K K - C t -     CR q C ( 1 e )   t t dq C - -    I e CR e CR d t CR R t -     V IR e CR R  V R +  V C =  t q -     CR V (1 - e ) C C

RL Circuits – Charging Current d I        L IR L dI I R dt dt d t L    L dI ( - IR)dt L dI   Integration constant dt  - IR L       n( - IR ) t K' R R R R      n( - IR ) t K' L L R R - t K'     L L - IR Ke (K e ) R - t     L IR Ke          At t 0, I 0 0 K K  R R - t - t        L L I R ( 1 e ) I ( 1 e ) R R - t      L V IR ( 1 e ) R R dI - t     L  V R +  V C =  V L e L dt

From Class 23 RC time constant Slide #4  =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.  t -  CR I e R   I  e 2.72 R -  1 e 0 . 37   - 1 I e R  ~ 0 . 37 R t t=RC t -    CR q C ( 1 e ) q   C  2 1.414    -1 q ( 1 e ) C  1 ~ 0 . 63 C  0 . 707 2 t Nothing to do with RC circuits t=RC

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.  R d I - t  L e d t L  dI   e 2.72 dt L -  1 e 0 . 37  dI  - 1 e dt L  ~ 0 . 37 L t t=L/R   R - t  I ( 1 e L ) R   I  R    - 1 2 1.414 I ( 1 e ) R  1 ~ 0 . 63  0 . 707 R 2 t t=L/R Nothing to do with RL circuits

From Class 23 RC Circuits – Discharging Charge Slide #5 q q d q      0 IR R 0 C C d t   CR dq - q dt dq 1   - dt Integration constant q CR t     n q - K' C R CR t -    K' q Ke CR (K e ) t -   CR q K e     At t 0, q Q Q K t -   CR q Qe t dq Q -    CR I e d t RC t Q -     CR V IR e R C  V R +  V C = 0 t q Q -    V e CR C C C

RL Circuits – Discharging Current Note special switch dI     0 L IR LdI -IRdt dt dI R L   Integration constant - dt charge I L R      n I - t K' L R discharge R - t    K' I Ke L (K e )         At t 0, I I K I 0 0 R R  R R - t - t   L L I I e or e t - 0  R I I e CR 0 R - t    V IR I Re L R 0  V R +  V L = 0 R d I - t    L V L - I Re L 0 d t

From Class 23 In Summary Slide #7 For both charge and discharge, Q, I,  V C , and  V R must be one of the following two cases: y y 0 t - y  RC y 0 e t y y  t -  RC y y (1 - e )  y can be Q, I,  V C , or  V R t

In Summary For both charge and discharge, I, dI/dt,  V L , and  V R must be one of the following two cases: y y 0 t - y  RC y 0 e t y y  t -  RC y y (1 - e )  y can be I, dI/dt,  V L , or  V R t