one last Circuit question......

[Semidevil]

ok, given the circuit where you have a 4.8 ohm resistor, 4H inductor, and a .25F capacitor all in a series, connected to a 160 V source, how do you find the s-domain expression for I.

so in S domain
Resistor = 4.8ohm
inductor = 4 S
capacitor = 1/.25 S or 4 S.

I did a regular KVL loop equation to get 4.8I + 4SI +1/.25S(I) =160V.

I need to get I, so I take I out of the left side, to get I(4.8 + 4S +1/.25S) = 160

now, I get I by itself:

I = 160/(4.8 + 4S + 1/.25S).

now I"m lost. what do I do next?

the answr the book gives is:

I = 40/(s^2 +1.2s + 1).

how?

 

[PrincessGuard]

Multiply numerator and denominator by .25.

 

[WhiteKnight]

That doesn't do it, there is an s^2 term in the book answer.

 

[Semidevil]

ok, I"m not sure if I left out some important material, but there is a switch right next to the Voltage source, saying

"the energy in the circuit shown is zero at the time when the switch is closed."

does this help?

 

[WhiteKnight]

That plays a huge role. Let me get back to you.

Edit: I thought that the problem sounded odd, as cap/ind problems are almost always time dependent. The reason is because at steady state (caps and inds charged), capacitors appear as open circuits and inductors appear as shorts.

 

[liv303]

Are you saying the capacitor is 4/S or 4S?

 

[Semidevil]

Originally posted by: liv303
Are you saying the capacitor is 4/S or 4S?

in the S domain, it is 1/cs, or 1/.25S, so eitehr that, or just 4S

 

[brunswickite]

4.8 + 4s + 4/s

multiple denominator by S = (4.8s +4s^2 + 4)
and then multiply num and deno by .25

 

[Semidevil]

Originally posted by: Semidevil

Originally posted by: liv303
Are you saying the capacitor is 4/S or 4S?

in the S domain, it is 1/cs, or 1/.25S, so eitehr that, or just 4S

edit: my bad, it is 4/S

 

[NutBucket]

The transform of the 160V source is 160/s since its a step input (ie it turns on when the switch closes).

 

[WhiteKnight]

Well then there you have it.

 

[PrincessGuard]

Originally posted by: WhiteKnight
That doesn't do it, there is an s^2 term in the book answer.

Whoops. Didn't notice that.

Anyway, WhiteKnight is right in that the switch is important. Your voltage source now has a unit step response, which has a Laplace transform of 1/s. so 4.8Is + 4Is + 4I/s = 160/s

Edit: Doh, beat to the punch

 

[NutBucket]

Glad I remember something. I finally "finished" my Circuits book last quarter. Stupid book took me 4 classes to go through. Felt quite good when I finished it