# Nodal analysis in simple circuit

I have a circuit to solve:

In this approach, I inferred the V1 from the parallel connection of voltage source. For the second node, I have applied the KCL.

I also tried to do it another way, by modifying the source E4 ( pushing it to the branch with G2 ) and then tried to apply nodal analysis.

Equation was like :

(G2+G1+G5)*V2=E4G2+E1G1-J

V2=(E4G2+E1G1-J)/(G2+G1+G5)

As You can see, both results differs by 'G5' in denominator. What is wrong?

• Please consider cleaning up the image and moving the formula's to the text field. Check the MathJax while you are at it, it'll improve readability even further. Dec 1 '13 at 16:23

$$(U - E_4)G_2 + (U - E_1)G_1 + J_5 = 0$$
$$U = E_1 \dfrac{G_1}{G_1 + G_2} + E_4 \dfrac{G_2}{G_1 + G_2} - \dfrac{J_5}{G_1 + G_2}$$