Using Kirchhoff's Laws to Find Currents, Source Current and Power Dissipated

[cschear87]

So based on the circuit and resistors etc, we've gotten equations for KVL. How do those equations translate into the other equation i5 = i1 + i2 + i3? I have another tutorial on this tonight but I really want to make a bit more progress.
For my own review I know that:
Right Loop: 40i2 -80i3 = 0
Middle Loop: 20i1 - 40i2 = 0
Left Loop: 10i5 + 20i1 = 10

I mean, is it simple algebra so each equation comes to 0, 0 and 10? Ie, i3 would be 1, i2 would be 2, i1 would be 4?

 

[tiny-tim]

hi cschear87!

Right Loop: 40i2 -80i3 = 0
Middle Loop: 20i1 - 40i2 = 0
…
I mean, is it simple algebra so each equation comes to 0, 0 and 10? Ie, i3 would be 1, i2 would be 2, i1 would be 4?

i'm not really following you

those two equations tell us the ratios: i₁ = 2i₂ = 4i₃

Left Loop: 10i5 + 20i1 = 10
So based on the circuit and resistors etc, we've gotten equations for KVL. How do those equations translate into the other equation i5 = i1 + i2 + i3?

the first 2 equations, in 3 unknowns, give you only the ratios between those 3 unknowns (because 3 = 2 + 1)

the last 2 equations (the equations with 1₅) give you a total of 4 equations in 4 unknowns, which enable you to solve them completely (because 4 = 4)

I have another tutorial on this tonight but I really want to make a bit more progress.

you need to ask for help on solving simultaneous equations