For Fig 3 (FA-9) use + to represent the direction of the currents shown in the f
ID: 1500550 • Letter: F
Question
For Fig 3 (FA-9) use + to represent the direction of the currents shown in the figure and - to represent the opposite directions. Let e = 25.0 V, R_1 = 47.0 Kilo-Ohm, R_2 = 96.0 Kilo-Ohm, R_3 = 88.0 kilo-Ohm and L = 15.0 micro-Henry. At time t = 0, i.e., immediately after switch S is closed, what is the value of current i1? Give your answer in the form "+/a bc times 10^(y) unit" B. At time t=0, i.e immediately after switch S is closed what is the value of current i2? Give your answer in the form "+/-a bc times 10^(y) unit". C. For t = infinity(i.e., a long time after the switch is closed)i1 = Give your answer in the form "+/a bc times 10 ^ (y) unit D. A long time after switch S has been closed it is suddenly opened. Answer this and the following problem. Immediately as the switch is Opened, what is the value of i_1? Give your answer in the form "a.bc" A E. Immediately as the switch is opened, what is the value of i2? Give your answer in the form "+/-a bc x 10^ (y) unit"Explanation / Answer
A) The inductor prevents a fast build-up of the current through it, so immediately after the switch is closed, the current in the inductor is zero. It follows that:
= 25/[( 47 +96)*103] =0.17mA
B) i2 =i1 = 0.17mA
C) After a suitably long time, the current reaches its steady state. The emf across the inductor is zero and we may imagine it being replaced by a wire. The current in R3 is i1 - i2 . Kirchoff's loop rule gives:
solving it simultaneously, gives = [25( 47+96)*103]/[(47*96 + 47*88 + 96*88)*106]
so, i1 = 2.19*10-4A
and = 1.28*10-4A
D) The left hand branch is now broken . We take the current in the branch as zero, immediately after the switch is opened. So, i1 = 0
E) The current in R3 changes less rapidly as it has an inductor in its branch. Infact as the switch is opened, it has the same vale as it had before the switch was opened. i3 = i1 - i2 = (2.19 - 1.28)*10-4 = 0.9*10-4 A
so current i2 is same but in the opposite direction = - 0.9*10-4 A
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.