Lecture30 - Chapter 6

# B sketch thevoltage current power and energy as

This preview shows pages 10–16. Sign up to view the full content.

b) Sketch thevoltage, current, power and energy as functions of time. c) Specify intervals when energy is being stored in/delivered by capacitor. Thevoltage pulseapplied across theterminals of a 0.5 F capacitor is μ v(t) = 0 t 0 v(t) = 4t volts 0 t 1 ≤ ≤ v(t) = 4e-(t-1) volts 1 t ≤ ≤∞

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
1111 Example 1 (2/3) a) v(t) = 0 V t 0 v(t) = 4t V 0 t 1 ≤ ≤ v(t) = 4e-(t-1) V 1 t ≤ ≤∞ i = Cdv/dt = 0 A t 0 i = Cdv/dt = 4C = 2 A μ 0 t 1 ≤ ≤ i = Cdv/dt = -4e-(t-1)C = -2e-(t-1) A μ 1
1212 Example 1 (3/3) -10.000 -8.000 -6.000 -4.000 -2.000 0.000 2.000 4.000 6.000 8.000 10.000 0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 2.7 3 3.3 3.6 3.9 time t v i p w b) v, i, p and w curves areplotted as functions of time c) Energy stored 0 t 1. Energy delivered 1 t ≤ ≤ ≤ ≤∞

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
1313 Example 2 (1/4) An uncharged 0.2 F capacitor is driven by a triangular current pulse, μ described by: i(t) = 0 t 0 i(t) = 5000t 0 t 20 s ≤ ≤ μ i(t) = 0.2 – 5000t 20 t 40 s ≤ ≤ μ i(t) = 0 t 40 s μ a) Derivetheexpression for the capacitor voltage, power and energy for each of thefour timeintervals needed to describe thecurrent b) Plot i, v, p and w versus t Initial voltage (Initial Condition) (IC)
1414 Example 2 (2/4) a) For t 0: v, p and w are all zero For 0 t 20 s: ≤ ≤ μ 2 t 0 9 6 t 10 x 5 . 12 0 τ d τ 5000 10 x 5 v = + = ( 29 3 12 2 9 t 10 x 5 . 62 ) t 5000 ( t 10 x 5 . 12 vi p = = = ( 29 4 12 2 2 9 6 2 t 10 x 625 . 15 t 10 x 5 . 12 ) 10 x 2 . 0 ( 2 1 Cv 2 1 w = = = - t t i 5000 ) ( =

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
1515 Example 2 (3/4) For 20 t 40 s: ≤ ≤ μ ( 29 ) t 5000 2 . 0 ( 10 t 10 x 5 . 12 t 10 vi p 2 9 6 - - - = = 5 6 2 6 3 9 4 12 10 t 10 x 2 t 10 x 123 . 0 t 10 x 5 . 2 t 10 x 625 . 15 w - - + - + - = 10 t 10 x 5 . 12 t 10 5 d ) 5000 2 . 0 ( 10 x 5 v 2 t
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern