# How to write the supermesh equations in this circuit

circuit analysis

Example 3.11 from Fundamentals of Electric Circuits (5th ed.) by C. Alexander and M. Sadiku:

I'm trying to solve this circuit via mesh analysis in order to challenge myself but I'm splitting my head here. I'm not asking you to solve the whole circuit, I'd just like some help with the writing of the equations.

It says that I have to use PSpice but I'm trying to do it manually.

Please understand that I just want to understand the method by which the question can be solved, rather than getting the whole answer itself.

I'll show you an easy way using mesh analysis plus one node. First look at the node at the top of the right-hand side \$2\Omega\$ resistor:

$$i_1+2A=i_1+i_3$$

from which you get immediately \$i_3=2A\$. Then you need two more equations for \$i_1\$ and \$i_2\$. Use the outer mesh and note that the current through the left-hand \$2\Omega\$ resistor is \$i_1+i_2+2A\$:

$$(i_1+i_2+2A)\cdot 2\Omega + i_1\cdot 4\Omega+2A (=i_3)\cdot 2\Omega=10V\tag{1}$$

The second equation comes from the mesh in the lower left of the circuit:

$$(i_1+i_2+2A)\cdot 2\Omega+i_2\cdot 1\Omega=10V\tag{2}$$

Solving (1) and (2) for \$i_1\$ and \$i_2\$ gives the desired result.