Hello!
I have a homework to deliver for one of my courses that consists of doing the nodal analysis of the following circuit, but I'm having a really hard time doing it. I made a schematic of the circuit on LTSpice and ran a simulation and I can't get the results shown there. I think my problem is getting to the equations. I got this:
(V_a+V_1-V_b)/R_2 + (V_a-V_b)/R_1 + V_a/R_4 =0,
(V_b-V_1-V_a)/R_2 + (V_b-V_a)/R_1 + (V_b-(V_c-V_3))/R_3 =0
(V_c-V_b)/R_3 + I_1+(V_c-V_2)/(R_6+R_5 )=0

The results I should be getting according to the simulation are: V(va): -0.47619, V(vb): -0.761905, V(vc): 1.33333
Can someone help me please?

 

Check your third equation carefully. I think you can spot the problem pretty quickly because you clearly know how to handle the presence of the voltage sources.

 

Check your third equation carefully. I think you can spot the problem pretty quickly because you clearly know how to handle the presence of the voltage sources.

Oh, I'm embaressed now. How did I not see this? Thank you
I suppose it is (V_c-V_b)/R_3 + I_1+(V_c-V_3-V_2)/(R_6+R_5 )=0 ?

 

uops, not that too. It's (V_c-V_3-V_b)/R_3 + I_1+(V_c-V_2)/(R_6+R_5 )=0 right?

 

Hello there,

Yes. If you swap R3 and V3 and ground Va, how would you write the equation then?

Edit:
Yes, V3 was missing because the current through R3 knowing Va and Vc also requires subtracting V3 to get the voltage across R3.
One way I ended up doing it was like this:
(Vc-E2)/(R6+R5)+(Vc-E3-Vb)/R3=-I1

(i use E2 and E3 instead of V2 and V3 for more clarity between what is constant and what is yet unknown).
(Also note that the use of 'camelback' notation eliminates the need for the messy underscores).