hw09solution

hw09solution - P835 t<0: t>0z 12 0111A 300ul50 = 1009...

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Unformatted text preview: P835 t<0: t>0z 12 0111A 300ul50 = 1009 iL = 3/150 = 20mA *D.5,(,{F 300T? 31.25mH 12L(0) = 20mA, 2L(oo) —« ~100mA 022 —- ~1— —— ————1—Og— — 64 x 106- w — 8000 rad/s ° _ LC " (31.25)(0.5) — ’ " _ 6 1 10 = 104'; a2 = 100 X 106 O! : 3170 = (200)(0.5) a2 ~ mg = (100 — 649106 = 36 x 106 31,2 = —10,000 i 6000 31 :2 -4000 rad/s; 32 = ~16,000 rad/s ‘ iL : If + Axle—40002: + Age—16,000t z'L(oo) = If = —100mA 234(0) =A’1+A’2+If 2 20 mA A'1+A'2— 100 = 20 so A'1+A'2 : 120mA £121“, dt Solving, A'1 = 160 mA, A; = —40mA (0) = 0 = ~4000A1 — 16,000A’2 iL = —100 + 1606400” — 40e‘16’000‘ mA, t > 0 4 P 8.37 [a] 2a m 5000; 0: == 2500rad/s m2 — mg 2 1500; 3 = 4 x 106; we = 2000rad/s R a=fi=2500; R=5000L 1 109 2:-—::4 16' L:————-———:r “’0 LC X 0’ 4x106(50) °H R = 25,000 (2 Lag?) = 03(0); %(50) x 10~9v§(0) = 90 x 10—6 vfm) = 3600; 116(0) = 60V (12(0) 60 w [c] m Aleqooot + Age—4000‘: =2 ~1000A1 —— 4000A2 = 12 Solving, A1 = 4mA; A2 = ~4mA i(t) = 4e“1°°0t * 4540001” mA 75 2 0 : ‘48—’100015 + 16€~4000t di ~4000t +1000): a x 0 when 166 = 46 or 830% = 4 t : Liaisons = 462.10 #8 [e] im = 4604621 —- 4(1-8484 = 1.89 mA [f] mt) : 5% = [—20e*1°°°‘ + soe-W] V, t 2 0+ I‘Io to+T P 9.6 u r: / V3, cos2(wt + qfi) dt ‘ to+T1 1 — - + -2— cos(2wt + 2gb) dt to 2 v2 to+T = —§"l {jiifiT dt + /t cos(2wt + 2gb) dt} Vnif 1 “71T+§;[ v2 ~21”— {T + E:— [sin(2wto + 47r + 2gb) — sin(2wto + 2¢)]} é) sin(2wt + 2¢) WT” H P 9.9 [a] The numerical values of the terms in Eq. 9.8 are Vm = 100, R/ L = 533.33, (AL 2 30 -W z: 50 ¢ = 60°, 0 = tan—1 30/40, 0 = 3687" 2': [-4.84653333‘ + 2008(400t + 23.13°)] A, t > 0 [b] Transient: component = ——1.84e”533'33t A Steady—state component 2 2 cos(400t + 23.13°) A [c] By direct substitution into Eq 9.9, i(l.875 ms) a 133.61 111A [d] 2A, 400rad/S, 23.13o [e] The current lags the voltage by 36.87 °. P 912 [a] 50Hz [b] 011‘: 00 I : LEO/‘9‘ = @/~ 90° 2 8.5/— 90°; 02. = -900 ij wL 340 w = . ‘ L = 4 [c] wL 8 5, w 09 40 400 [e] ZL = M = 32109 ...
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This note was uploaded on 07/29/2008 for the course ECE 376 taught by Professor Milenkovic during the Summer '06 term at Wisconsin.

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hw09solution - P835 t<0: t>0z 12 0111A 300ul50 = 1009...

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