Did I do my loop analysis correctly?

[naivy]

Homework Statement

Homework Equations

The Attempt at a Solution

If we were to call the bottom right loop I₁, the top loop I₂, and the bottom right loop I₃. I got the following:

I₁ = 1mA
I₂ = 6mA
I₃ = 2mA

Which gives me a final answer of I₀ = -1mA.

Is this correct?

 

[lewando]

No, it is not correct.

 

[phinds]

checking your answer is trivial. All the loop currents become immediately obvious once you assume you have I0, and then you can get the voltages across the resistors and when you add them up, you'll find that the voltage across the 20V source is not 20V, so clearly you have the wrong answer. Learn how to check you work. It's often just this simple.

 

[naivy]

I fixed it and got:

I₁ = 3mA
I₂ = -1mA
I₃ = -1mA

Which gives me a final answer of I₀ = 4mA.