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

In summary: 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.
  • #1
darksyesider
63
0

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?
 

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  • #2
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.
 
  • #3
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. :smile:
 
  • #4
gneill said:
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. :smile:

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?
 
  • #5
phinds said:
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 :smile:
 
  • #6
gneill said:
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 :smile:

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

Thanks for that correction ... I might have confused him.
 
  • #7
phinds said:
Thanks for that correction ... I might have confused him.

No problem, always glad to help where I can.
 
  • #8
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.
 
  • #9
darksyesider said:
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.
 

1. What is Kirchoff's law problem?

Kirchoff's law problem refers to a set of principles that describe the behavior of electrical circuits. These principles were developed by German physicist Gustav Kirchoff in the mid-19th century and are widely used in the analysis of complex electrical circuits.

2. What are the two laws of Kirchoff's law problem?

Kirchoff's law problem consists of two laws: Kirchoff's current law (KCL) and Kirchoff's voltage law (KVL). KCL states that the total current entering a junction in a circuit must equal the total current leaving the junction. KVL states that the sum of all voltage drops in a closed loop must equal the sum of all voltage sources in the loop.

3. Why are Kirchoff's laws important?

Kirchoff's laws are important because they provide a systematic method for analyzing and solving complex electrical circuits. They are also fundamental principles that form the basis for many other laws and theories in the field of electrical engineering.

4. How do you apply Kirchoff's laws to solve a problem?

To apply Kirchoff's laws, you first need to draw a circuit diagram and identify all the elements in the circuit, such as resistors, voltage sources, and current sources. Then, you can use KCL and KVL to set up a system of equations and solve for the unknown variables. It is important to follow the direction of current flow and assign proper signs to voltage drops and sources.

5. Can Kirchoff's laws be applied to any type of circuit?

Yes, Kirchoff's laws can be applied to any type of circuit, including series circuits, parallel circuits, and more complex circuits with multiple loops and junctions. However, they are most commonly used for DC circuits. For AC circuits, additional considerations must be made due to the presence of complex impedance and reactance.

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