# Mesh Analysis has failed to solve this circuit

I built the following circuit in LTSpice and found each mesh currents to be (which also matches the answer sheet provided by my professor):

i1: 9A
i2: 8A
i3: 11A
i4: -6A

However, I am unable to solve each mesh current using Mesh Analysis following the sign conventions.

Here's my approach:

Mesh 1: i1 = 9A
Mesh 2: R1*(i2 - i1) + i4*3 + R2*(i2 - i3) = 0
Supermesh: R2*(i3 - i2) + R3*i4 = 0
Also: i3 - i4 = 17 ===> i3 = 17 + i4

where R1=6ohm; R2=4ohm; R3=2ohm

If I substitute in mesh current from the spice simulation, the supermesh matches where Mesh 2 doesn't. However, I checked many online sites and followed the sign conventions, but I am not able to get it to work, where did I do wrong? ## 1 Answer

ok, there was an error in the original question, the current dependent voltage source has a gain of "-3*i4", not 3*i4.

After correcting the sign, the formula is solved as expected.

• How did your LTspice simulation match the prof's answers then when you had the wrong circuit? – DKNguyen Feb 27 at 0:09
• when the circuit matches the original drawing (with wrong 3*i4), the mesh current i2 was something like 43/7. After I put the minus sign fo (-3*i4), the mesh current i2 became 8A, and there was 6V across R1. – user97662 Feb 27 at 21:48