EE411_HW6_Soln

# EE411_HW6_Soln - v 4 ) ( = + At t=0 + , switch is switched...

This preview shows pages 1–4. Sign up to view the full content.

Ans: Assume the voltage across the 1/25 F capacitor is v c (t). It is obviously that before switch is closed, v c (0 - )=0. Since the voltage across the capacitor cannot change instantaneously, we have v c (0 + )=v c (0 - )=0. In order to calculate dt dv c ) 0 ( + , we apply KCL at the right plate of the 1/25F capacitor 0 ) 0 ( 0 ) 0 ( ) 0 ( 4 ) 0 ( ) 0 ( 25 1 = = = = Ω + + + + + dt dv i i v dt dv c L L c c Apply KVL, we have j s t v dt t dv dt t v d t v dt t dv dt t v d t v dt t dv dt d t v t v dt t dv dt t di L t v t i c c c c c c c c c c c L c L 608 . 4 125 . 15 5000 ) ( 250 ) ( 4 121 ) ( 50 ) ( 5 . 2 ) ( 400 121 ) ( 100 1 50 4 ) ( ) ( 25 1 4 1 ) ( 6 4 ) ( ) ( 25 1 50 ) ( ) ( ) ( 2 , 1 2 2 2 2 ± = = + + = + + = Ω + + + × Ω + = + + So we can write )) 608 . 4 sin( ) 608 . 4 cos( ( 20 ) ( 125 . 15 t B t A e t v t c + + = 6467 . 65 0 608 . 4 125 . 15 ) 0 ( 20 0 20 ) 0 ( = = + = = = + = + + B B A dt dv A A v c c

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

View Full Document
So () 0 ) 608 . 4 sin( 4117 . 16 ) 608 . 4 cos( 4 5 4 ) ( ) ( )) 608 . 4 sin( 6467 . 65 ) 608 . 4 cos( 20 ( 20 ) ( 125 . 15 125 . 15 > + + = Ω = + = t t t e t v t i t t e t v t c t c
Ans: (a)At t=0 - , we have V v 4 ) 0 ( = Since the voltage across a capacitor cannot change instantaneously, we have V

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: v 4 ) ( = + At t=0 + , switch is switched to the left, because the inductor current cannot change instantaneously, we have ) ( = + L i And hence 8 ) ( 5 . 4 ) ( − = ⇒ = Ω + + + dt dv V dt dv C (b)This is a parallel RLC circuit. We have 3 1 2 1 1 2 1 , 1 2 1 2 2 , 1 j s LC RC ± − = − ± − = = = = = ω α So )} 3 sin( ) 3 cos( { ) ( t B t A e t v t + = − Using the initial conditions, we have 309 . 2 3 4 8 3 ) 1 ( ) ( 4 ) ( − = − = ⇒ − = + − = = = + + B B A dt dv A v )} 3 sin( 309 . 2 ) 3 cos( 4 { ) ( t t e t v t − = −...
View Full Document

## This note was uploaded on 02/24/2011 for the course EE 411 taught by Professor Lee during the Spring '07 term at University of Texas.

### Page1 / 4

EE411_HW6_Soln - v 4 ) ( = + At t=0 + , switch is switched...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online