Trouble Understanding RLC Circuits: Detailed Explanation for 250W Power Release

[Juraj]

I'm having real trouble understanding some concepts in RLC circuits.

If I have a circuit like this. The effective voltage is 120 V. What is the required frequency for resistor to release power of 250 W?

I want to really understand this on a deeper level so please make the explanation detailed. I know that the power is P = VI but what voltage should (maximum or effective) I use, what current? How to calculate current if I have voltage? Why can't I just use P = V^2/R or P = V^2/Z? I'm really bothered by this and AC circuits seem very complicated. And what about the voltage drop in series circuit, does that affect the result?

And also, when is P = VIcos(phi) used? Can i use it here? And what if I wanted to calculate the energy released by the inductor or capacitor?

 

[magoo]

I think you are lost in the equations. The V that you need is what occurs across the resistor. Not having that, go with the power equation in terms of current.

A better way to start is to ask - what value of current will deliver 250 W through the resistor? Watts = I^2 R

So now we have the current. You have an impedance that is complex and will change depending on frequency.

You need to write out the components of the impedance as a function of frequency. The magnitude of the impedance is Z.

With an effective voltage of 120 V and an impedance of Z, write the equation for the current.

 

[jim hardy]

I want to really understand this on a deeper level so please make the explanation detailed.

You already understand more than you think you do. Just you're looking for an instant one step solution.

Authors of textbooks try to make you think in steps . So they give you problems that require two or more of them.

There's several ways to approach this one, and you should work it a few times coming at it from different angles.

I'd say first, as magoo suggested , figure what must be the current through the resistor , and then what must be the total impedance of the circuit to result in that much current. Pythagoras will tell you the reactance necessary, so at what frequency does 185 mh and 65 uf make that reactance?

And what if I wanted to calculate the energy released by the inductor or capacitor?

Inductors and capacitors do not dissipate energy - go back to your basics.

And also, when is P = VIcos(phi) used? Can i use it here?

Now that's interesting. 250 = 120 X current X cos(phi) gives you phi... Pythagoras again ?See, you knew that already didn't you ?
Much of learning is discovering what we already know.

Have you learned rectangular and polar notation yet ? That's the mental muscle this exercise is trying to build.

old jim

 

[Juraj]

It seems more clear now, thanks!