# Solution4 - UNIVERSITY OF CALIFORNIA AT BERKELEY EECS...

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UNIVERSITY OF CALIFORNIA AT BERKELEY EECS Department Page 1 of 6 EECS 40/42/100, Spring 2007 Prof. Chang-Hasnain Homework #4 Due at 6 pm in 240 Cory on Wednesday, 2/14/07 Total Points: 100 Put (1) your name and (2) discussion section number on your homework. You need to put down all the derivation steps to obtain full credits of the problems. Numerical answers alone will at best receive low percentage partial credits. No late submission will be accepted expect those with prior approval from Prof. Chang-Hasnain. 1. Hambley, P3.25 [8 points] F C C C eq μ 3 / 2 / 1 / 1 1 2 1 = + = The charges stored on each capacitor V C Q V V C Q V C V C Q eq 4 8 8 12 2 2 1 1 = = = = = ! = μ 2. Hambley, P3.43 [8 points – 2 per graph] 2 2 0 0 )] ( [ )] ( [ 2 1 ) ( ) ( ) ( ) ( ) ( 2 1 ) 0 ( ) ( 1 ) ( t i t i L t w t i t v t P ft t v i dt t v L t i L L L t L L t L = = = = + = ! ! ! " #! #" \$! ! \$ % & ( *+,-. / *0. !"## !\$%# !\$## !%# # %# \$## \$%# "## # " & ( ) +,-./ 0 +1/

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UNIVERSITY OF CALIFORNIA AT BERKELEY EECS Department Page 2 of 6 W (Joul) t (sec) 225J 3. Hambley, P4.7 [9 points] Before t=0, v(t)=0 After t=0, apply KCL to the top node, mA dt t dv C R t v 1 ) ( ) ( = + (1) [3 points] The solution is of the form [1 point] ) 100 exp( ) / exp( ) ( 2 1 2 1 t K K RC t K K t v ! + = ! + = (2) substitute (2) into (1) => K1=10 [2 points] Another boundary condition v(0)=0 => k1+k2=0 =>k2=-k1=-10 [2 points] Thus, ) 100 exp( 10 10 ) ( t t v ! ! = [1 point] 4. Hambley, P4.8 [9 points] The voltage can be written as ) / exp( ) ( RC t V t v i c ! = [3 points] At t=0, V V v i c 50 ) 0 ( = = [3 points] At t=30, ) / 30 exp( ) 30 ( RC V v i c ! = => R= 4.328M [3 points] 5. Hambley, P4.9 [10 points] During the charging interval, s C R 10 1 1 = = !
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• Spring '07
• Chang-Hasnain
• RC circuit, Electrical network, Thévenin's theorem, Norton's theorem, Current Source

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