# AC circuits.

1. May 2, 2013

### hyddro

Hi, so I have a homework problem and I don't know how to approach. I am given a circuit, with an AC source, a resistor ( 2 Ω) and a unknown circuit element (that could be an inductor or a capacitor).
I am also given a graph with the Voltage amplitud across the AC source (Which happens to be 100)., I am given the I_ave, which i converted to I ( 20 A). From the graph I calculated the angular frequency (about 340 rad/s). I also found the reactance of the unknown element. Then the question ask for the unknown element: is it an inductor or a capacitor? They also give a hint: they say that increasing the current will help you find whether is an inductor or a capacitor? (How so?)

I am stuck here, I don't know how to do this. I tried doing a phasor diagram but I doesn't seem to help. I just don't know what they mean by 'increasing the current'. Doesn't the current increase by itself? or do they mean the I amplitude? And how would that help me find the element?

Related equations.

V = I Z ( Z = sqrt( R^2 + (XL - XC )^2)
i=I cos(wt)
v_r = IR cos(wt)
w = 2∏*f

Any help will be appreciated.

2. May 2, 2013

### Staff: Mentor

Can you post the exact question (preferably scanned)? It's a bit hard to understand exactly what they are saying and asking...

3. May 2, 2013

### hyddro

Sorry, here it is. Ty.

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4. May 2, 2013

### Staff: Mentor

Much better

They say increase the *frequency* of the source, and this is what causes Irms to increase. So that tells you whether the component is a capacitor or inductor. Which is it and why? What are the formulas for the impedance of an inductor and a capacitor?

Last edited: May 3, 2013
5. May 2, 2013

### hyddro

Ok, so the impedance for both would be Z = sqrt ( R^2 + X^2) , where X can be either the impedance of a capacitor or an insulator.

So for a capacitor, Z = sqrt ( R^2 + (1/wC)^2) and for the insulator Z = sqrt(R^2 + (wL)^2)...

ok I see now how the angular frequency would change the impedance. If w increases, then Z for a capacitor decreases, if w increases with an inductor then Z increases.

So now what? I don't know neither the capacitance nor the inductance of the element and also, do I have to increase the w to a specific value? or can it be arbitrary? (say 400rad/s)

thank you

EDIT: Oh, but I can find them cause I know the angular frequency and the reactance of the element.
I don't have the actual reactance with me now (I left my hw at school and Im at home now) Lets pick an arbitrary value, say that the reactance of the element is 40 Ohms.

Then Xc = 1/wC so C=1/wXc (C = 1/340*40) right? similarly, XL = wL, so L = XL/w (L=340/40)...

is this right?

Last edited: May 2, 2013
6. May 2, 2013

### rude man

How did you determine the reactance of the 'element'? You can only determine it by I = V/Z.

7. May 2, 2013

### hyddro

EWell, there has to be only one element, so either Xc or Xl = 0, if one of the =0 then the other is present. Z = sqrt( R^2 + (Xl-Xc)^2), which is either sqrt( R^2 + Xl^2) or Sqrt( R^2 + Xc^2) , or simply sqrt(R^2 + X^2)
where X is either 1/wC or wL.

EDIT: In case you meant the actual value, V=100, I=20A so Z =5 = Sqrt(2^2 + X^2) , and just solve for X.

EDIT2: so I actually found the angular frequency and X for the element again. w=314.2 rad/s and X=sqrt(21)=4.58 ohms

8. May 2, 2013

### rude man

OK, all that looks good.

9. May 2, 2013

### SammyS

Staff Emeritus
By the way:

Not only does the problem say to increase the frequency rather than the current, the problem states that the root-mean current is 14.1 A . So, you were given the r.m.s current, not the average current. (The average current is zero.)

You were correct in converting the r.m.s current of 14.1 A to a sinusoidal amplitude of 20 A .

10. May 2, 2013

### hyddro

Thank you, yes I forgot that they were actually giving me the RMS current. You mention something interesting though, the average current is zero. This is because the current oscillates between 20 and -20 right? so the average is 0. Just making sure I know my facts. Ty.

11. May 2, 2013

### SammyS

Staff Emeritus
Yes.

Before you scanned and posted the exact question, I was very puzzled regarding that value for average current.

12. May 2, 2013

### hyddro

Oh ok thank you. I am trying to approach this problem in so many different ways that I got stuck already, So here is my attempt to solving this.
1. We know that if w increases, I increases. I = V/Z , so in order for I to increase, Z has to decrease (as V is constant). (holy crap my head is hurting at this point) Now, for Z to decrease (due to an increase in w) the element must be a capacitor because Z = Sqrt(2^2 + (1/wc)^2), if w increases then Z decreases, hence I increases. Is this analysis correct? It sounds ok to me, but there is one thing tough, why would they say 'increasing w would result on an increase on I' Clearly, for an inductor, increasing w will result on a greater Z, hence I decreases (cause I=V/Z). Any ideas? Thank you.

EDIT: Wait, now that I read the problem, I think they say the Current increases due to the increase in w. Are they saying that they actually increased w and what they saw was that I(rms) increased? If so then the element is a capacitor right?

13. May 2, 2013

### SammyS

Staff Emeritus
Right.