How do I find the current through each resistor using Kirchoff's laws?

[darksyesider]

Homework Statement

See attached image.

Suppose I want to find the current through each resistor…how would I do so?

Homework Equations

Kirchoffs eqns … sum of voltages around every loop is zero

The Attempt at a Solution

1. The first problem I have with this, is that i am not sure how many currents there are. I put arrows in different colors the currents that I think there are. Could someone verify this step?

2. If (1) is correct, then I think that the blue current = red + green current

3. Next, I would attempt at using kirchhoffs law on the smallest loop, and the loop which does not involve the top two resistors (the one with 5 resistors and 2 batteries in it). Then i would solve for current using a matrix.

So generally speaking, is this a correct method?

 

[phinds]

You have too many currents shown (red, blue, green = one too many). You have one little loop in the upper part another loop in the lower part. Just draw currents for those two loops.

 

[gneill]

You've identified that there will be three different current values to be found. Three unknowns implies that you need three independent equations in order to solve for them.

There are several possible approaches, the most basic of which is to write KVL around the obvious loops (yielding two independent equations), and writing KCL at one of the nodes in order to give a third equation. That is essentially the steps that you've described.

 

[phinds]

You've identified that there will be three different current values to be found. Three unknowns implies that you need three independent equations in order to solve for them.

There are several possible approaches, the most basic of which is to write KVL around the obvious loops (yielding two independent equations), and writing KCL at one of the nodes in order to give a third equation. That is essentially the steps that you've described.

Yes, that would work, but why would you want to go to 3 equations in 3 unknowns if he can just do what I suggested and have two equations in two unknowns?

 

[gneill]

Yes, that would work, but why would you want to go to 3 equations in 3 unknowns if he can just do what I suggested and have two equations in two unknowns?

That would be the mesh current approach which, based upon the way the question was presented by the OP, is probably a chapter or two further along in his studies. I figured that he'd just been introduced to basic KVL and KCL at this point.

Besides, you still need to write a third equation (essentially the same KCL equation) in order to determine the green current from the two mesh currents, even with the mesh approach

 

[phinds]

That would be the mesh current approach which, based upon the way the question was presented by the OP, is probably a chapter or two further along in his studies. I figured that he'd just been introduced to basic KVL and KCL at this point.

Besides, you still need to write a third equation (essentially the same KCL equation) in order to determine the green current from the two mesh currents, even with the mesh approach

Damn. You're right on both counts. Of course you already knew that didn't you

Thanks for that correction ... I might have confused him.

 

[gneill]

Thanks for that correction ... I might have confused him.

No problem, always glad to help where I can.

 

[darksyesider]

Yes, I am just being introduced to Kirchoff's, so I have not heard about "mesh".

sorry, but what is the difference between: KVL and KCL??

For the 3 equations, I have the blue = red +green and applying kirchhoff on both small loops.

 

[gneill]

Yes, I am just being introduced to Kirchoff's, so I have not heard about "mesh".

sorry, but what is the difference between: KVL and KCL??

For the 3 equations, I have the blue = red +green and applying kirchhoff on both small loops.

There are two Kirchhoff laws: KCL and KVL. The Current Law and the Voltage Law. One pertains to the sum of currents that enter/leave a node, the other to the sum of potential drops/rises around a closed loop. Your text should define both and provide examples.