Question

In the adjoining circuit, the switch, which had been closed for a sufficiently long time for steady state to be reached, is opened at time t = 0. Determine the following, as a function of time:

(a) The current I L(t) through the inductor, and (b) The voltage v R(t) across the 1k Ohm resistor.

I=0 Rs=5.12 [26) Vs= + Ro= 1 k 2 20 V 1 H 0000 vr(t)

Answer 1

solerioni Giren circuit is an Rg=52 t=0 following: ato 31926) + Đ V=20volt TH vele Ro= { V (H) At t=0-(moment just before switching); the efervalent circent is as following: (inductor benares as short-cincest at statening steady state), Rs=52 + ② vs zovolt * ct) S.C. Ro= So, IL CO-) = 20 = 4 Amp. Rg Due to current inentia property of indector, the ennent through indretor remaine same after sevitching, { Cot) = q co-)= 4 Amp [where, plot)=cument through indector just after switching, After suntching, at initial state the indector behaves as open-cincent with coment source in parallel. But, at steady state the inductor current is zero as there se no energy source alres sunitching So, I (0)= 0 Amp. Ello) ROS + zikr Volt) 1

The curent (t) can be be expressed as, Pe (t) = f (as) - {12 (20) - Plotzet where, 2= time constant of the cincerit= Roo 10-3 sec. نے بے 1X103 10-3 -103 = 4 e 50.941 )= 0-40-43e and, Vr(t) = Rpq (t)= 18103x4Xe lost -1034 - 4000e PACH) + Ro =land Velt) (AW 4034 a) consent through indectorie, P,(t) = 46-lost b) voltage across Ro=1kr reejetor is VR (t) = 40000 (Ane)