Let’s consider the upper mesh current named i, the left side one named
i2 and the right side one is i1.
Thus we get v = R2*(i1 – i2), which corresponds to a superposition
theorem.
Let’s take away the current source (put an open circuit)
We then have the following equations:
-
In the upper loop we get: V1 – R1*i – R3*(i + i2) = 0
-
In the left loop we get: V2 – R2*i2 – R3*(i + i2) = 0
In those two equations, the only unknowns are i and i2.
We have two equations and 2 unknowns so we can solve the system.
We solve for i in the first equation to get it in terms of i1, and we
find
Then we substitute this i in the second one and we get
We can then substitute the value of i2 for v and find v = R2*(i1 – i2)