What Is the Correct Approach to Solve This Loop Analysis Problem?

[ee_ess_ee-kid]

Homework Statement

http://i.imgur.com/pVIMw.png"

Homework Equations

The Attempt at a Solution

I called the top left loop i1, the top right loop i2, the bottom right loop i3, and the bottom left loop i4. I have all of these currents going clockwise in my work. An attempt to do loop analysis has left me with the following equations:

i₄=(2V_x)/(1K)
i₁-i₂=2mA
i₃=-4mA
-i₂(4kΩ)=V_x

With this, I used KVL along the top loop going clcokwise, which got me:

-2(i₁-i₄) - 4i₁ - 4i₂ - 1i₂ - 8(i₂-i₃) = 0
Solving this got me:
i₂=(-25/44)mA

Then, V₀=(8kΩ)(-25/44 mA)=-1.76V

Can someone please help me figure it out? When I go and try to check it, my work gets pretty weird...Pretty sure this is wrong. Can someone please help me find my mistake?

 

[gneill]

Verify the polarity of Vx.

 

[ee_ess_ee-kid]

I was confused by that.

Should it be i₂(4κΩ)=V_x?

Redoing my work gets me V₀=11V, which looks better. I'll check to see if that answer makes more sense

 

[gneill]

Current through a resistor causes a voltage drop (+ to -) in the direction that the current flows. What's the assumed direction of i2?

 

[ee_ess_ee-kid]

Current through a resistor causes a voltage drop (+ to -) in the direction that the current flows. What's the assumed direction of i2?

I have all the currents going clockwise.

I have i₂ going from left to right on that resistor.

 

[gneill]

I have all the currents going clockwise.

I have i₂ going from left to right on that resistor.

So then...

 

[ee_ess_ee-kid]

So then...

So then it should be V_x=i₂(4κΩ)

 

[gneill]

So then it should be V_x=i₂(4κΩ)

Correct.

 

[ee_ess_ee-kid]

If I use that, I get the following:

i₁=13mA
i₂=11mA
i₃=-4mA
i₄=88mA

Using these values, I fail to get a correct check using KVL on the top loop. I can't get ƩV=0...

 

[gneill]

If I use that, I get the following:

i₁=13mA
i₂=11mA
i₃=-4mA
i₄=88mA

Using these values, I fail to get a correct check using KVL on the top loop. I can't get ƩV=0...

I get a different value for i2 (I didn't check the other currents) when I solve your equations. You'll have to post your work in detail if we're to see what's happened.

 

[ee_ess_ee-kid]

I get a different value for i2 (I didn't check the other currents) when I solve your equations. You'll have to post your work in detail if we're to see what's happened.

Actually, I found it myself. Turns out I did the following:

i₁-i₂=2mA → i₁=2-i₂

Which is wrong :p

Fixing this error, I got a value of i₂=-14.6667=-44/3, if i₂ were going clockwise.

 

[ee_ess_ee-kid]

Thanks for all of your help, I really appreciate it!