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I'm a first year engineering student who has a problem with harder nodal analysis problems.

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Consider the circuit in the attached image. The usual way to deal with the voltage sources in the upper left branch is to make a supernode. However, one of the nodes (node 1) is necessarily common to the supernodes. I need to know how to handle these situations with nodal analysis and without repositioning the sources. I'd be really glad if someone helped me.

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Don't get thrown off by having multiple voltage sources attached to the same node: just follow the super-node procedure, and recognize that it's ok to combine a super-node with another node/super-node to make a "super-super-node" (or just a bigger super-node).

In your case, you will eventually have a super-node which contains nodes 1, 2, and 3, and 2 other equations which describe the relationship between (v1,v2) and (v1,v3).

This gives you 3 equations and 3 unknowns, which can be solved using some algebra.

Finding these equations is left as an exercise for the reader (feel free to ask questions if you get stuck somewhere)

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