1 / 12

RC Circuit: Charging Capacitor

Instantaneous charge q on a charging capacitor:. a. R. b. V. i. C. +. +. -. -. RC Circuit: Charging Capacitor. At time t = 0: q = CV(1 - 1); q = 0. At time t =  : q = CV(1 - 0); q max = CV. The charge q rises from zero initially to its maximum value q ma x = CV.

kasi
Télécharger la présentation

RC Circuit: Charging Capacitor

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Instantaneous charge q on a charging capacitor: a R b V i C + + - - RC Circuit: Charging Capacitor At time t = 0: q = CV(1 - 1); q = 0 At time t = : q = CV(1 - 0); qmax = CV The charge q rises from zero initially to its maximum value qmax = CV

  2. q Qmax Capacitor a R = 1400 W Rise in Charge b V i 4 mF Time, t 0.63 Q + + t - - Example 1. What is the charge on a 4-mF capacitor charged by 12-V for a time t = RC? The time t = RC is known as the time constant. e = 2.718; e-1 = 0.63

  3. q Qmax Capacitor a R = 1400 W Rise in Charge b V i 4 mF Time, t 0.63 Q + + t - - Example 1 (Cont.) What is the time constant t? The time t = RC is known as the time constant. In one time constant (5.60 ms in this example), the charge rises to 63% of its maximum value (CV). t = (1400 W)(4 mF) t = 5.60 ms

  4. As charge qrises, the current i will decay. a R b V i C + + - - RC Circuit: Decay of Current Current decay as a capacitor is charged:

  5. Capacitor i I 0.37 I Current Decay a R t b Time, t V i C + + Consider i when t = 0 and t =  . - - Current Decay The current is a maximum of I = V/R when t = 0. The current is zero when t =  (because the back emf from C is equal to V).

  6. Capacitor i a R = 1400 W I 0.37 I Current Decay b V i 4 mF t Time, t + + - - Example 2. What is the current i after one time constant (t = RC)? Given R and C as before. The time t = RC is known as the time constant. e = 2.718; e-1 = 0.37

  7. q Qmax Capacitor Capacitor i Rise in Charge I 0.37 I Current Decay Time, t t 0.63 I Time, t t Charge and Current During the Charging of a Capacitor. In a time t of one time constant, the charge q rises to 63% of its maximum, while the current i decays to 37% of its maximum value.

  8. a R a R b b V C V i C + + + + - - - - RC Circuit: Discharge After C is fully charged, we turn switch to b, allowing it to discharge. Discharging capacitor. . . loop rule gives: Negative because of decreasing I.

  9. a R b V i C + + - - Discharging Capacitor Note qo = CV and the instantaneous current is: dq/dt. Current i for a discharging capacitor.

  10. a R b V i C + + - - Prob. 45.How many time constants are needed for a capacitor to reach 99% of final charge? Let x = t/RC, then: e-x = 1-0.99 or e-x = 0.01 From definition of logarithm: 4.61 time constants x = 4.61

  11. a 1.4 MW i R b 1.8 mF C V 12 V + + - - Prob. 46. Find time constant, qmax, and time to reach a charge of 16 mC if V = 12 V and C = 4 mF. t = RC = (1.4 MW)(1.8 mF) t = 2.52 s qmax = 21.6 mC qmax = CV = (1.8 mF)(12 V); Continued . . .

  12. a 1.4 MW i R b 1.8 mF C V 12 V + + - - Prob. 46. Find time constant, qmax, and time to reach a charge of 16 mC if V = 12 V and C = 4 mF. Let x = t/RC, then: From definition of logarithm: x = 1.35 Time to reach 16 mC: t = 3.40 s

More Related