Uncovering the Unknown Circuit Element: An Exploration

[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.

 

[berkeman]

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.

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

 

[hyddro]

Sorry, here it is. Ty.

 

[berkeman]

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?

 

[hyddro]

thanks for replying!
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 youEDIT: 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 homework at school and I am at home now) Let's 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?

 

[rude man]

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

 

[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

 

[rude man]

OK, all that looks good.

 

[SammyS]

...

, I am given the I_ave, which i converted to I ( 20 A) ...

...They also give a hint: they say that increasing the current will help you find whether is an inductor or a capacitor ...

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 .

 

[hyddro]

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 .

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.

 

[SammyS]

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.

Yes.

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

 

[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?

 

[SammyS]

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?

Right.