How to find Voltages and currents of the following circuit

[itzernie]

Homework Statement

The circuit of the given problem is attached to this post (jpg file). All info is given in the photo.
Problem: find V_A, V_B, I_A.

Homework Equations

Ohms law
KCL equations
P = VI or V^2/R

The Attempt at a Solution

- First, I noted that V_B = 9 - V_A.
- next, i set up a KCL equation at V_A:
-.004V_B + V_A/30 + (2V_A -18)/30 = 0
- i plugged in V_B:
-.004(9-V_A) + V_A/30 + (2V_A -18)/30 = 0

- Solved for V_A = 6.115 V
- Therefore V_B must = 2.885 V (given everything so far is correct

- by Ohm's law, I_A = V_B / 15 k ohms
- I_A = 0.1923 mA

- so at this point I have values for all i need to solve the problem, but to check if i was right I wanted to check consv of power.

- KCL at V_A node = .1923 + 11.54 = I_B
I_B = 11.7323 mA

When I checked the power on all 4 items in this circuit, the power did not check out to zero, so somewhere I messed up but I have no idea where.

 

[gneill]

...somewhere I messed up but I have no idea where.

I'd look to how you handled the resistances versus the controlled current source magnitude. You've dropped the "k" on the resistors implying that currents will be in mA, but left the controlled source multiplier as is.

 

[phyzguy]

I think you have the right answer for VA and VB, but, as gneill says, you have messed up A and mA on the currents, so IB is definitely wrong. Also, make sure you pay attention to the signs on the powers.

 

[itzernie]

Thanks for the help and time!
but Ok so seeing V_A and V_B believed to be correct is reassuring and leads me to believe that somewhere it is just a small error when dealing with powers.

But ok so in this case either my source calc or I_A must be wrong since I_B calculations come afterwards...

so I_A = 2.885V / 15Kohm = 0.1923 mA
source: .004(2.885V) A = 0.01154 A which can be translated to 11.54 mA ??

I feel like I need new glasses right now lol

 

[gneill]

I see Va being larger, much closer to 9 V. Vb will be pretty small. The currents should be small too, all of them less than a milliamp.

 

[itzernie]

I see Va being larger, much closer to 9 V. Vb will be pretty small. The currents should be small too, all of them less than a milliamp.

WAIT ! I think I see it. Is it because in my KCL equation where I solve for Va... By only dividing by 30 those are milliamps whereas the source is Amos so to balance it I need to change the .004(9-Va) to 4(9-Va). Which is the issue you first stated ?

 

[gneill]

It is! It's safer to first write the node equation with the k's still in, then multiply through by 1000 to eliminate them. That catches all the conversions.

 

[phyzguy]

My bad. I made the same mistake as the OP. Ignore my earlier post and listen to gneill.