Kirchhoff's Rules, system of equation problem

coile3

I came up with three equations, to find three different currents in a DC circuit, using Kirchhoff's loop rule, but when I solved them as a matrix in my calculator the bottom row becomes all zero's and the first two rows do not appear to be in "rref" form. I solved the system of equations by hand and when I add the solution from the first two (my new equation) to the third I get 0=0. Is this because they are dependent? If I use Kirchoffs junction rule to get an additional equation I can substitute the junction equation for any of the original three and get the answers. Should I always use the junction rule to find at least one of my equations, and is this problem due to not having used an equation from the junction rule originally or is it an occasional occurance and normally using any three equations (following Kirchhoff's rules) will give me the results I need?

thanks for the help.

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James R

Homework Helper
Gold Member
Probably, two of the three equations you obtained using the loop rule are equivalent, which means that without the junction rule you don't have enough information to solve the problem.

Essentially, you're trying to solve 2 equations for 3 unknowns, so you get an infinite number of possible solutions. The addition of the junction rule narrows it down to one solution.

coile3

Thanksl that is exactly what has happened, I get an infinite amount of solutions so, Does that mean I should always use an equation generated by the junction rule?

James R

Homework Helper
Gold Member
Does that mean I should always use an equation generated by the junction rule?
In these types of problems it is usually necessary, since the currents are related.

Gokul43201

Staff Emeritus
Gold Member
You MUST use the junction rule (explicitly or implicitly). You will have an insufficient number of linearly independent equations without it.

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