# Homework Help: Average power dissipated in resistor

1. Apr 8, 2015

### Bluestribute

1. The problem statement, all variables and given/known data
Find the average power dissipated in the 30 Ω resistor in the circuit seen in the figure if ig=7cos20,000tA.

2. Relevant equations
KVL/KCL equations
P=VI* (possibly) or I^2(R)

3. The attempt at a solution
I tried to do a mesh, but got I(60-j130) = 0, which isn't right . . . I'm assuming I find the current through the resistor and just do I^2(R)?

File size:
4.4 KB
Views:
288
2. Apr 8, 2015

### Staff: Mentor

You'll want to find the RMS current through the resistor if you're looking for average power. The source specification would appear to be a time-domain peak current...

Show your work!

3. Apr 8, 2015

### Bluestribute

I = I

30I(-j40) + 30I(30) - I(j10) = 0

Doesn't quite add up . . .

4. Apr 8, 2015

### Staff: Mentor

I don't see the controlled voltage source in there, and I don't see a contribution from the independent current source ig from the first mesh. What are your mesh equations?

5. Apr 8, 2015

### Bluestribute

That was my one mesh equation . . .

6. Apr 8, 2015

### Staff: Mentor

But there are two loops...

7. Apr 8, 2015

### Bluestribute

But wouldn't the other one just be Ig? Or is it 5mH(I-Ig) = 0? Converting mH to ohms of course

8. Apr 8, 2015

### Staff: Mentor

Well, you can call it ig if you wish, but it's still a separate mesh current.

In the figure, i1 = ig and iΔ is the net current through the inductor.

9. Apr 8, 2015

### Bluestribute

Right right. So across the inductor, it'd be (I1 - I)10j = 0? And then for the other mesh, 30I(-j40) + 30I(30) - I(j10) = 0?

10. Apr 8, 2015

### Staff: Mentor

No, I is the net current through the inductor. The first mesh is already "solved" for its current since it's identical to that of the fixed source. Thus $i_\Delta = i_g - i_2$.
Remember that there are two mesh currents flowing through the inductor. And the source is dependent on $I_\Delta$, not I.

11. Apr 8, 2015

### Bluestribute

Wait, you are very confusing right now.

So I = Ig - I2? Ok, I can dig that.

So for my other mesh, do I replace I with I2? And solve for I2?

12. Apr 8, 2015

### Staff: Mentor

You just wrote an equation for I above! Use that.

13. Apr 8, 2015

### Bluestribute

Wait, you lost me again. What two equations am I using? Am I solving I∆? Do I solve I∆ then use I^2(R) to find power?

14. Apr 8, 2015

### Staff: Mentor

What current is flowing through the resistor? It's $i_2$, right? So that's what you need to find. That's the mesh current for the second loop. $i_\Delta$ is just the net current through the inductor, and happens to be the "sense current" controlling the dependent source. You don't necessarily have to solve for it explicitly, but you do need to replace it with its equivalent in terms of mesh currents otherwise you'll have another variable on your hands.

The first mesh current is effectively already solved for since it's identical to $i_g$. You don't need to write a mesh equation for it. But you do need to use the auxiliary equation for $I_\Delta$ since that's needed to write the equation for the second loop (for the controlled source).

15. Apr 8, 2015

### Bluestribute

30(Ig - I2)(-j40) + 30(Ig-I2)(30) - (Ig-I2)(j10) = 0?

I just replaced I∆ with the equivalent current of Ig - I2

But I still have one less equation than variables . . . So this gives me one equation two variables. Adding in the Ig relationship gives two equations three variables.

16. Apr 8, 2015

### Staff: Mentor

The only variable I see in your equation is $I_2$.

17. Apr 8, 2015

### Bluestribute

Oh yeah, it says what Ig is.

So when I do my calculations, I can use 7 for Ig, right, since its angle is 0?

I just need to make sure my first attempt is correct. Since, you know, Mastering Engineering. I already failed one for putting the magnitude of j instead of the complex form of the impedance (it didn't ask for the complex form, just magnitude).

18. Apr 8, 2015

### Staff: Mentor

You can. Just keep in mind that 7 is the peak value of the source current, not the RMS value. So you'll end up calculating the peak value of the current through the resistor.
Yeah, I'm not a big fan of computer based quizzes myself.

19. Apr 8, 2015

### Bluestribute

So use 7/root2 as I go through just to be safe . . . got it.

Yep, this is pretty much the only online place where I actually learn something. Which is a shame 'cause that's what Mastering is SUPPOSED to do.

20. Apr 8, 2015

### Staff: Mentor

If you want you can use 7 and find the peak current, then convert peak to RMS at the end. Saves carrying the √2 through all the maths. It's just a scaling factor for a sinusoidal waveform.

21. Apr 8, 2015

### Bluestribute

For space, I'm just using I as my variable. So I plugged in 7 for Ig and solved that long equation (30(Ig - I2)(-j40) + 30(Ig-I2)(30) - (Ig-I2)(j10) = 0)

-8400j + I1200j + 6300 - 6300I -70j + i10j = 0
I(6300 + 1210j) = (6300 - 8470j)

Gives me a peak of 1.6455 and an Arms of 1.16354

That gives me a power, using I^2(R), of 40.614 W

Did I screw up anywhere?

22. Apr 8, 2015

### Staff: Mentor

Yup. You've got (Ig - I2) flowing through all the components. It doesn't. I2 is the mesh current that flows through all the components of the loop (with Ig flowing through the inductor too, of course, since it's a component shared by the two loops).

23. Apr 8, 2015

### Bluestribute

So only the inductor and dependent source use I∆ and the rest use I2?

24. Apr 8, 2015

### Staff: Mentor

I∆ is a parameter of the dependent source. I2 flows through it (and through the capacitor, and through the resistor). The inductor has two mesh currents because it borders two meshes.

25. Apr 8, 2015

### Bluestribute

So

I2(-j40) + I2(30) + (I2 - (Ig - I2)) = 0?

Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted