Electronic – Finding current using Kirchoff Law, but getting unsolvable system

circuit analysisdckirchhoffs-laws

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Hello, the original circuit above is where I am trying to find I1, and I simplify it the figure below and assuming the following current directions.

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Using Kirchoff current and voltage laws I end up with

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However, plugging in the equations into my calculator it says there is no solution. Is it with my kirchoff current equations (first 4 equations) because if I add up all current law equations I end up with 0 = 0. Can anyone tell me what I am doing wrong? Thanks for any help.

EDIT:

As other mentioned I need more KVL equations. But I also need my KVL to be independent loops, so I need at least 3 independent KVL equations.

Best Answer

If you use KVL in the other loop (36v i5 and i2) then use that, the other kvl equations and two of the kcl equations it should work.

Adding all the kcl equations should give 0=0. They don't include the voltage so they can't actually solve for anything here.

Using star-delta transforms and mesh analysis can make it a bit easier to solve (transform the delta that doesn't have I1 in it to a star/wye).

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