Alternating current

builder_user

Hello.This is my new task.
1. The problem statement, all variables and given/known data
Find e(t),i(t),Ul(t),Ur(t),Uc(t),Urc(t),Url(t).
Find reactive power and complex power.

2. Relevant equations
What to do with Ulc(t)?


3. The attempt at a solution
C=200microfarad
L=3millihenry
r=4 Ohms
Ulc(t)=17.89sin(1000t-64)

I've done this
Zc=-j/wC
Zl=jwL
I've deleted L and C and added Zc and Zl to scheme.What is next?
I can't find w because I do not have e(t).

Here my original scheme.

Attached Thumbnails

   

gneill

There's no Ulc(t) shown in the first figure. Are the diagrams supposed to represent the same circuit redrawn, or are there two circuits to solve?

What are the units for the given Ulc(t)? Is the amplitude in volts? Is t in seconds? Is '64' an angle in degrees or in radians? How about the '1000'? Is it in radians per second? Degrees per second? Something else?

builder_user

It's one circuit.

V
17.89 - amplitude
t - seconds
64- degrees
1000 -w(sec-1)

gneill

Well, you can pick the value of ω out of the given expression for Ulc(t). Presuming that the 1000 is 1000 degrees/second, you can convert that to radians per second for ω.

That will allow you to calculate the impedance for the series LC. If you then express Ulc as a complex phasor, you should have no difficulty computing the complex current phasor for the current through LC. Since the whole circuit is series connected, the same current flows through the R as well, and you can determine e as a complex phasor.
Convert back to sin(ω*t + θ) form if desired.

Given the current and voltages, you should have no trouble calculating the power.

builder_user

64*=0.35pi?
1000 = 5.5pi?

w will be the same for all u(t) and i(t) and e(t)?

gneill

Yes, ω will be the same across the board.

You might find it to be a good idea to carry a few more decimal places for intermediate results. Round the final results at the end. So

64° --> 1.117 radians
1000°/sec --> 17.453 radians/sec

builder_user

Is I(t)=Ulc/zl+zc=
17.89sin(5.5pi*t-0.35pi)/(j*5.5pi*L+(-j/5.5pi*L)=17.89sin(17.5t-1.12)/(17.5jL-j/(17.5L)?

gneill

I think a couple of your L's should be C's in the above.

Convert the Ulc(t) to phasor form so you're working entirely in the frequency domain. But you're on the right approach.

builder_user

exp?
17.89*(exp^j(17.5t-1.12)-exp^-j(17.5-1.12))/(2*j(17.5j-j/17.5C))

To get u for every element of the circuit i(t) must be multiplyed by every resistance?

gneill

In the frequency domain the time dependent angle disappears. In complex form you can write the voltage as:

Ulc = 17.89V*(cos(φ) + j*sin(φ))

where φ is your phase angle, -64° = -1.117 radians

Solve for the current by dividing this voltage by the impedance ZL+ZC as you indicated earlier. Then current x individual impedances for the individual voltages.

You didn't say whether the given voltage Ulc was peak or rms. Did the original problem statement mention it?

builder_user

So,current is the same for all elems.
For Urc = I*(Zr+Zc)?

And How to find e(t)?

I don't know what is rms.All I know is Ulc - instanteous voltage

gneill

The current is the same for all series connected components. So the overall voltage is given by I*Ztotal. That will equal your e (in complex phasor form).

It seems that your two circuit diagrams have the order of the components changed, so that makes it hard to understand what is meant by Urc or Ulc.

builder_user

It's made to find LC.I(t) will not change because all elems are the same.

How to find complex power and reactive power?Amplitude e(t)/Ze,
where Ze=Zl+Zr+Zc?

Amplitude for every U&e -> x *(cos....)?

builder_user

How to find active and reactive power?

gneill

If you have the voltage source, e, in complex phasor form, and the current, I, also in complex phasor form, then the apparent power is p = eI*, where I* is the complex conjugate of I.

The components of p are the real and reactive components of the power. Do a search on "power triangle" if you need more information about apparent, real, and reactive power.

builder_user

It's means that if I have
e(t)=B*sin(wt-q)
and I(t)=A*sin(wt-q) the result will be like this

p=B*sin(wt-q)/A?

gneill

No. First of all, the voltage and current waveforms will not have the same phase angle, because of the impedance having both real and imaginary parts. Secondly, you want to be dealing with complex values in the frequency domain, not sines and cosines in the time domain. There should be no t's involved.

Perhaps I'm making an assumption that I shouldn't be making. Do you know what phasors are? How about their representation as complex values?