The circuit has been running for a long time prior to the switch closing at = 0. The supply voltage is 100v2 sin(100t) V The complete response of the i (t) is of the form: ij (t) = X,e(-X2t) + Y2 sin(100t + Y2) Amps where X1, X2, Y1 , Y2 are unknown. 1) Determine the instantaneous value of i / at the moment of switching (t=0). 2) Determine the values of Y, and Y, in the forced response component of ij (t). Determine the unit of Y2 . 3) Determine the values of X, and X2 in the natural response component of i (t).

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The circuit has been running for a long time prior to the switch closing at = 0.The supply voltage is 100v2 sin(100t) V.
The complete response of the i¿(t) is of the form:
iL (t) = X1e(-X2t) + Y2 sin(100t + Y2) Amps
where X,,X2, Y, , Y, are unknown.
1) Determine the instantaneous value of i / at the moment of switching (t=0).
2) Determine the values of Y, and Y, in the forced response component of ij, (t). Determine the unit of Y,
3) Determine the values of X1 and X2 in the natural response component of iL (t).
t=0
50 0
0.5 H
Vs(t)
50 0
Transcribed Image Text:The circuit has been running for a long time prior to the switch closing at = 0.The supply voltage is 100v2 sin(100t) V. The complete response of the i¿(t) is of the form: iL (t) = X1e(-X2t) + Y2 sin(100t + Y2) Amps where X,,X2, Y, , Y, are unknown. 1) Determine the instantaneous value of i / at the moment of switching (t=0). 2) Determine the values of Y, and Y, in the forced response component of ij, (t). Determine the unit of Y, 3) Determine the values of X1 and X2 in the natural response component of iL (t). t=0 50 0 0.5 H Vs(t) 50 0
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