(a) Find the current i(t) as a function of time. (b) Find the charge and energy
ID: 1924682 • Letter: #
Question
(a) Find the current i(t) as a function of time.
(b) Find the charge and energy stored in each capacitor at t = 0 and for t -> INFINITE.
Explanation / Answer
a)When the switch is at A for long time the current i given by i=4/1000=4mA after the switch position is changed from A to B, we have 12x10^-6F and a 4x10^-6F in series., and this combination is in parallel with other(top) 4x10^-6F So C=(12 || 4) + 4 =>C=4.33x10^-6F applying KVL gives 1000i1+(1/C)int(i1)=0 differentiating the above equation gives., 1000di1/dt+(1/C)i1=0 =>di1/dt+230.95i1=0 solution of this is i1=c x exp(-230.95t) but at t=0- ie., just before changing the position of switch..we have i=4mA substituting t=0 in i1 equation gives 4x10^-3=c x exp(0) =>c=4x10^-3 substituting this c value in i1 gives i1=4x10^-3exp(-230.95) where i1=i(t) for the circuit.. b)at t=0 the energy stored in each capacitor is zero.. W=0.5CV^2=0 at t=infinite energy stored in the circuit is given as W=-4x10^(-3)exp(-461.9t) J
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