Solving Electrical Circuits: Find Voltage Vx

[erezb84]

Homework Statement

I need to find the voltage Vx.
Vs = V0*cos(wt)
given: w,R,C,L,V0

I thought doing KVL,KCL but got stuck...
is this the way to solve this? is there another way?

Thanks!

 

[Simon Bridge]

Have you tried Kirkoff's Laws?

 

[erezb84]

This is what i wrote, i have tried KVL KCL but got stuck, is this the way or there is another "trick"?

 

[ehild]

It is the way and you can apply tricks only in special cases. What was the
problem in detail?

You can determine the resultant impedance when you see parallel or in-series elements. It can happen that a capacitor and an inductor make a resonant circuit. In this case the resultant impedance is infinite if they are connected parallel, and zero when they are in series. ehild

 

[erezb84]

Can you please elaborate the last sentece...?

 

[Simon Bridge]

He's suggesting that you simplify the circuit to just a few impedences - like right nest to the Vx you have a cap and an inductor in parallel - you can combine their impedences to a single component.

Remember how you used to do this when it was just resistances?

I cannot tell how you tried to apply kirkoffs laws from what you wrote - KVL and KCL tells me nothing...

By brute-force you have something like 5 loops and 8 nodes. Since I don't know how you did your working I don't know where you got stuck ... if you don't say what you did you can only get the most general of answers.

There are only two ways of doing this sort of problem - Kirkoffs Laws, and simplifying the circuit to an equivalent with fewer impedences and then applying kirkoff.

 

[erezb84]

Many thanks! I will try again!

 

[ehild]

There are only two ways of doing this sort of problem - Kirkoffs Laws, and simplifying the circuit to an equivalent with fewer impedences and then applying kirkoff.

"Kirkoff" is Kirchhoff. http://en.wikipedia.org/wiki/Gustav_Kirchhoff. And KCL, KVL mean Kirchhoff's circuit laws "Kirchhoff' Current Law"and "Kirchhoff's Voltage Law".

ehild

 

[ehild]

Can you please elaborate the last sentece...?

The impedance of a capacitor C and inductor L in series is Z=jωL+1/(jωc).
If LCω²=1 the impedance is zero, and you can substitute it with a short.
When a capacitor and inductor are connected in parallel, the impedance is jωL/(1-ω²LC) infinite, and can be omitted from the circuit.
The diagram is too complicated for a homework. I think the data are given is such way that some simplification is possible.

So what are the numerical data for the circuit?

ehild

 

[erezb84]

Thank for the explanation!
Indeed in my case w=1/sqrt(L3*C3)

So, Vx=0?

 

[ehild]

Thank for the explanation!
Indeed in my case w=1/sqrt(L3*C3)

So, Vx=0?

As no current can flow through Rx, Vx = 0. It was simple, wasn't it?

ehild

 

[erezb84]

With your guidelines it was :)

 

[Simon Bridge]

"Kirkoff" is Kirchhoff. http://en.wikipedia.org/wiki/Gustav_Kirchhoff. And KCL, KVL mean Kirchhoff's circuit laws "Kirchhoff' Current Law"and "Kirchhoff's Voltage Law".

ehild

Spelling is just not my thing! <sigh>
I should have realized what the TLAs meant you are right.
Good call on the resonance.

 

[ehild]

Spelling is just not my thing! <sigh>
I should have realized what the TLAs meant you are right.
Good call on the resonance.

First I thought that you learned about Kirchhoff's Laws in Russian.

And what is TLA? (I hate abbreviations).

That circuit was so complicated that it had no sense without resonant parts.

ehild

 

[Simon Bridge]

First I thought that you learned about Kirchhoff's Laws in Russian.

Nah - on Star Trek ... I learned the James Tiberius Kirk-off Laws :) (We come in peace - aside: set phasers on stun.)

And what is TLA? (I hate abbreviations).

You'll like this one - it's toungue-in-cheek when people use them too much. It means "Three Letter Acronym".

That circuit was so complicated that it had no sense without resonant parts.

I guess - I was being a bit cruel pushing K's laws (see how I cunningly avoid spelling, um, it?) ... but applying them to those little loops would have shown the same thing and pain is such a good teacher.

Of course, generating relief is good too.

I see we were told that w was given - just not what it was given as: which is probably what would have cued me in on it post #1.

Anyhoo - I enjoyed watching you work. Ta.

 

[erezb84]

Me too! Nice to learn some new and good intuitions...

 

[ehild]

I was being a bit cruel pushing K's laws (see how I cunningly avoid spelling, um, it?)

Just use KCL and KVL as anybody else here...
Your post is a good lecture for me in Contemporary English - having read it about 10 times I still do not understand half of it. Ta.


@erezb84: I hate when a student starts to solve a problem with plugging in data, except AC circuits. For most of them, that is the best start. Plug in data, evaluate, simplify.

ehild

 

[Simon Bridge]

Oh that's annoying ... oh well, as long as it was fun.
(pm me if you don't figure it out.)