find voltage between two nodes

builder_user

if it's cramer's method...
I know this method but I only use it in programming.I solve all equtations in MathCAd.And then I show result without numbers and then the final result.The result without numbers is very big sometimes.

gneill

Okay, even better.

Attached is an example, using MathCad, of solving the loops by writing the loop equations in matrix form (which can be done by inspection, and is (almost) foolproof). It's very quick.

Attached Files

Schem1.pdf (67.3 KB, 2 views)

builder_user

Intersting.I didn't know about it in Mathcad
all results are the same as the results in my method of countour currents

thank you for your help.

gneill

The most interesting part, I think, is that you can write the equation quickly by inspection.

For the impedance matrix, the terms on the diagonal are just the sum of the impedances (resistances in this case) in the given loop. The off-diagonal terms are just the negative of the impedances that are shared by the loops indexed by the matrix entry. So in this case, for example, R2 is shared by loops 1 and 2, so z₁₂ and z₂₁ are both -R2. Note that the impedance matrix is symmetrical about the diagonal, so it's very quick to fill in.

The voltage vector is just the sum of the voltage source rises in the given loop (where a rise is taken to mean that a given voltage source goes from - to + in the direction of the loop current).

builder_user

I've got it.I compared elements of matrix with my equations a few minutes ago.