# Writing the Nodal and Mesh equations for large circuit and large supermesh

Here's my circuit:

simulate this circuit – Schematic created using CircuitLab

I have defined the node 'voltages' and the mesh current directions and the currents themselves. What I want to do is calculate the nodal and mesh equations for this circuit given the information above.

Here's my work at the nodal analysis: $$KCL\;\;V_1:\;\;{ {{V_1-V_2}\over R_2} +{{V_1-V_3}\over R_1} + {V_1\over R_3}= 0}$$ $$KCL\;\;V_2:\;\;{ {-I_b} +{{V_2-V_1}\over R_2} -I_a = 0}$$ $$KCL\;\;V_3:\;\;{ {{V_3-V_1}\over R_1}+I_a +{{V_3-V_4}\over R_4} = 0}$$ $$KCL\;\;V_4:\;\;{ {{V_4-V_3}\over R_4} +{{V_4}\over R_5} - I_c = 0}$$ As far as I can tell, those should be correct.

My next problem is how to get the equations for the mesh currents. What my issue is, is at the super mesh(s?) formed by Ia and Ib. I'm not sure how to get the mesh currents if those are there.

To summarize, I'm pretty sure my voltage/nodal equations are correct but I'm not 100% sure about that. I don't know how to get the mesh current equations if those independent sources are in this particular configuration.

If anyone could help I would greatly appreciate it. Thank you!

• For node V1, you've omitted the current through R3. Haven't looked any further! – Chu Oct 11 '18 at 6:23

For a supermesh enclosing both current sources you need to come up with three equations. One equation will be a KVL equation around a loop that encloses $$\I_A\$$ and $$\I_B\$$. I see only one loop that satisfies that requirement and has no current sources on the loop itself.
The second equation states the relationship between $$\I_A\$$, $$\I_1\$$, and $$\I_3\$$. The third equation similarly states the relationship between $$\I_B\$$ and mesh currents. These last two equations you should be able to write by inspection.