Question

The switch in the given figure moves from position A to position B at t = 0 (please note that the switch must connect to point B before it breaks the connection at A, a make before break switch). Determine i(t) for t > 0. Also assume that the initial voltage on the capacitor is zero and / = 3.0 A. t=0 A i(t) B 10 mF I 2012 102 0.25 H The value of i(t) = [AeBtc(Dt - E°)]u(t) A where A = C (Click to select) B= and E = COS sin

Answer 1

At t=0 the switch position is changed from A to B

To know the status of elements at t=0 we will find them t<0

t<0

we have a current source and and two resistors and an inductor all are connected in parallel so the after a long time the whole 3A current flows through only inductor.

A i(1) Ι 20 Ω 10 Ω 0.25 Η ell

so when the position of switch is changed from position-A to position-B

Now the circuit dosent have a constant current source the circuit contains 3 components they are 1 capacitor, 1-resistor and an inductor.

The current through the inductor doesn't change suddenly so the current through the inductor at t=0 is 3Amp The circuit is represented like this

100/5 1022 0.25 S ele 3/5

The above circuit is laplace representation of the elements. The capacitor will be represented as $\frac{1}{SC}$

The inductor will be represented as   

The current source will be represented as  

S

To make the calculations easy we will do some source transformation technique we will convert the current source to the voltage source by doing the

The voltage in series with the inductor is given by

V = (3/s)*(0.25s) =3/4 Volts

100 10 0.255 S 13% V lets simplify Capacitor & desistor Z- 2, Zz Z, +Z2 = 100 X 10 100 Stlo 100 t10 v Z Total 3%u 100 Stlo + s 4 3 (5+10) 52+105 + 400

3 (5+5) + 15 S2+ lost 400. 3 (5+5) 5²+105+25+ 375 + 15 Sa+105 +25+375 3 (5+5) 15 (5+5) + 375 (5+5)²+ 375 -54 3e sin 19.36t) & 15 15 -st cos (19.36t) 19.36 3 est sin (19.36t) + 0.27 & cos (19.367) est - 3 sin (19.36t) + 0.77 COS (19-36t)) -5t e x3.096 ( 3 sin (19:36t) + 0.77 cos (19.36 €)) 3.096 3.096 3:096 est sin (19.36t - o)) cos' (13.096) = 0.24 in radians. A= 3.096, B=-5 c = sin, D=19.36 E- 0.24 radian.
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