Question

Question 2: 0.5 Mark The switch in the circuit below has been closed for a long time before it opened at ta0. Find i(t), io(t and vo(t) for t>o. t-o 2Sz \l02 డa O.1a 20A

Answer 1

The circuit from time too to to will be 40% Vo Elv 20A at time to the inductor will be opened so that the the total Gorrent will frow through the inductor only. . 1, 10-) = 20 Amps. at time t=0, the switch s, is opened and from the basics of network theory, we know that the inductor will not allow the sudden change an current 2.1, 10) = 1, (0.1 = 20 Amps. Vlo) - Ov At time t-ot to tas, the circuit will be as. Rea 320 long your we can modify the resistor network into single resiston branch network, where Req= (10/160)+2 = Collag) + 2 = 8+2= los lotho The equivalent circuit will be as

O & Applying KVL to loop A, we get Į die + k beq = 0. + diet Recreo - . Je + du det hele - iH - I, e (2.To = 1/01-2 [ {(t) = 20e-st Amps. I - Inductor current , 8(61= 20e-stimees o the original circuit after t o ct ال2 م

By vello corrent division sole, we will obtain Polt) = ult). 10 10+40 = - 20.0-5t to sos C iott) = -4e-st Amps. I for txo Voltage, Volt) = 4,45.40 = -4e-st (60) Volt) = - 160.e-5t Volts.