need bit of help to see if this bit is right cheers

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mlm1234
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#1
Report Thread starter 10 months ago
#1
Use Laplace Transforms to derive an expression for the current i(t) flowing in the circuit below, given i(t)=0 when t=0.

E1 = 2v
R1 = 4ohms
C1 = 0.125
L1 = 1 H

Switch and I (t) is unknown.


E1 = Vr + Vl + Vc

E1/s = R1i(s) +L1si(s) + i(s)/sC

2/s = 4i(s) + si(s) + i(s)/0.125s

2/s = i(s)(4 + s + 1/0.125s)

i(s) = 2/s(4 + s + 8s)

i(s) = 2/4s + s^2 + 8)

i(s) = 2/(s^2 + 4s + 8)

then i can go onto find w/(s+a)^2 + w^2
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mqb2766
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#2
Report 10 months ago
#2
Sort of. Your capacitor seems to oscillate it's order 1/s -> s -> 1/s
But the final transfer function expression looks ok.
Last edited by mqb2766; 10 months ago
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