(a) How long will it take for the current to reach 67% of its maximum value?(b) What is the maximum energy stored in the inductor?(c) How long will it for the energy stored in the inductor to reach 67% of its maximum value?
a) Time constant L/R 4.6 microseconds
oubaas: are you able to describe why for the inductor you do not use the a million-e^even if and for the resistor you do? i'm purely attempting to appreciate the thoughts previously for my midterm. thanks!
TL/R, The current will rise to 67% in one time constant. energy.5 L I^2
(a) steady state current I V/R 24/130 0.1846amp (67%)(I) (0.67)(0.1846) 0.1237amp I [ V/R ][ 1 - e ^ ( - RT / L) ] T [ - L/R ]ln[ (V/R - I)(R) / V ] T [ - 6.70E-4/130 ]ln[ (24/130 - 0.1237)(130) / 24 ] T 5.715E-6 sec ans (b) max magnetic energy stored in the inductor E (1/2)(L)(I ^ 2) E (1/2)(6.7E-4)(0.1846 ^ 2) E 1.14E-5 J ans (c) I sqrt(0.67 * E) I 0.002 764 amp T [ - L/R ]ln[ (V/R - I)(R) / V ] T [ - 6.7E-4/130 ]ln[ (24/130 - 0.002 764)(130) / 24 ] T 7.774E-8 sec ans
