Question

Problem:

The current in and the voltage across a 5 Hinductor are known to be zero fort <= 0. The voltage across the inductor is given by the graph in fort >= 0. A. Write the expressions that describe the current i(t) in piece-wise linear representation in suitable intervals. Find the current in the inductor at t2 s. B. Derive the expressions for the inductor power and energy. Use the passive sign convention. Sketch the current, power and energy waveform below the given waveform. v (V) 100 1 2 3 4 5 61(s)

Answer 1

2:54 vendi at 22 J udt 100 7 Dz -100 -100 + v= - 1007 ; ost sa =100t 2005 22763 = 100 ; 337 55 = -100++600; 557 36 ® iz Ž Svat= 7/3 Svet 11 an -loot ; olzs toot-200 ; 12ts3 100 j 33735 -100 t ttoo ; sztsb. no (-10t² ; osten 2 10t²-tot; 15233 207 332ss. - 107² +1207 552236

put t=2 in 1st 23 Internal L (2) = lot²_tot = loxy- 90x2 = VOLA to - ooz - 40A 350 360 - 100 so 7 29 ot ® Power = VA [A =stot ²) (Hoot) ; ostsi 11007-200) [1022_40 t) ; 13733 100 (2ot) ; 33755 Hoot +60o) (-10724120t); 55th 6 Power=8 = (watt) 1000 7² į ostsi 100043 600ot + groot , 15753 2000t ; 357 35 (100073 - 18000+²+720oot ; 537st

Cubic graph of PE? 35 ооо 2 ортоо bboo 1 ооо — Looo Energy = Spodt now integrate pe — 250 44 o <ts) = 25 1- 2 соо4° 4-ooot; 1 32 33 = |соо — у з< +35 - 25. t1 — kooot's teoct:55 к. за ч оео Ecz Joule 25ooo 9 Фо 2250 2 50 te