How Much Power Is Dissipated in Each Resistor in a Multiloop Circuit?

[Cisneros778]

Homework Statement

Three resistors, R1 = 32 Ω, R2 = 45 Ω, and R3 = 60 Ω, are connected in a multiloop circuit, as shown in the figure. Determine the amount of power dissipated in the three resistors.

Homework Equations

loop law
junction law

The Attempt at a Solution

(1) i1 +i2 +i3 = 0

(2) 9 - 45 i2 + 32 i1 = 0

(3) 15 +60 i3 + 9 - 45 i2 = 0

when you use the loop law, don't you have to go the same direction with every loop?
In the equation (3) it is going clockwise, and in equation (2) it is going counter-clockwise.
Is this wrong?

 

[gneill]

You don't have to go the same direction with every loop. All you have to do is respect the potential drops/rises as specified by the chosen current directions (as indicated by the arrows) as you traverse the components during your "tour" around the loop.

 

[tiny-tim]

Hi Cisneros778!

when you use the loop law, don't you have to go the same direction with every loop?
In the equation (3) it is going clockwise, and in equation (2) it is going counter-clockwise.
Is this wrong?

No, it doesn't matter which way round you go …

if you went the other way round one loop, everything would be multiplied by -1, wouldn't it?

btw, it might be easier to take the outside loop rather than the bottom loop (the outside loop is the sum of the other two), since it has one less term in it (and one less chance of making a mistake! )​

 

[Cisneros778]

Thank you so much. I got the answers correct!