Kirchhoff's Law Homework: Help Needed with 2 Loops

[smalls]

Homework Statement

Homework Equations

hello,i have started working on it and i got the first 2loops.i just want to make sure i am on the right path before i continue to find the third loop.which i think i'm..so please,can anybody help me out here?pleas

The Attempt at a Solution

i have attached my attemped solution.
thank you

 

[Yosty22]

It might be easier to see if you label all of your loops and junctions. Including the big outer loop, you can write a total of 4 loop rules, as well as two junction rules. Try labeling the loops and junctions, as well as determining the sign of each current going into/away from the junction.

 

[Simon Bridge]

Why I1-I2 through R3

Note: there are two Kirkoff's Laws ... you appear to be trying to apply the node law simultaneously with the loop law. That is not best practice - especially with more complicated circuits where it is easy to get confused.

Yes - label the loops and nodes (junctions) on the diagram.
You will need as many equations as you have currents to find.

 

[smalls]

It might be easier to see if you label all of your loops and junctions. Including the big outer loop, you can write a total of 4 loop rules, as well as two junction rules. Try labeling the loops and junctions, as well as determining the sign of each current going into/away from the junction.

like this?

 

[smalls]

Why I1-I2 through R3

Note: there are two Kirkoff's Laws ... you appear to be trying to apply the node law simultaneously with the loop law. That is not best practice - especially with more complicated circuits where it is easy to get confused.

Yes - label the loops and nodes (junctions) on the diagram.
You will need as many equations as you have currents to find.

The thing is,this is a whole new topic to us and we were only given 2 examples and we were given this to do.and those examples were only with 2loops

 

[Yosty22]

Also pay attention to the direction of the current you draw. If I1 and I2 are directed toward each other, how will there be any current in the third (right-most) loop? Once you get the current directions figured out, take it one step at a time loop by loop. Keep the sign conventions in mind for writing your equations, and then it just becomes some algebra to solve for each current.

 

[smalls]

Also pay attention to the direction of the current you draw. If I1 and I2 are directed toward each other, how will there be any current in the third (right-most) loop? Once you get the current directions figured out, take it one step at a time loop by loop. Keep the sign conventions in mind for writing your equations, and then it just becomes some algebra to solve for each current.

so what i did was wrong i guess..:'(...really confused now.because they was i have started was the way we have been tought and i have been watching videos on how to go about it and still don't get it..

 

[Yosty22]

Granted, all that will change in the math is a negative sign in a junction rule, so if you labeled each loop and junction you can start with the loops. Start by calling something loop 1 (usually either the left-most loop or the entire outside loop) and start writing the loop rule. Start at the EMF source and work your way in a direction you choose. (Direction you go around the loop will change the signs, but if you keep it consistent, you will get the same answer in the end).

 

[smalls]

please i am a beginner and i do not understand anything you just said.this is not something like an exam.its just an exercise we were ask to try hands on.so all i want is for someone to take me through it step by step and explain to me..that's all i am asking for please...thank you

 

[gneill]

Begin by labeling your diagram to identify the loops. Then identify the nodes from which branches, well, branch from Then add a current for each unique branch. Each component should end up having a unique current flowing through it. Like this:

For convenience I chose to number the currents to correspond to the resistor number in the branch (the exception is the current I₁ that flows through both R₁ and R₃ because they are in the same branch -- I picked the lower resistor number for the current number).

You could add a forth loop that traverses the outer perimeter of the circuit, but it is not necessary for solving the circuit: once you have every component "touched" at least once by some loop, you have enough loops.

Now you need to apply your KVL rules to write the equations. Do a "KVL walk" around each loop summing the potential changes due to voltage sources and the individual currents in the components. Then write KCL for each of the nodes. You'll find that you need to use one less node than you've identified (try it, you'll see why).

 

[smalls]

Begin by labeling your diagram to identify the loops. Then identify the nodes from which branches, well, branch from Then add a current for each unique branch. Each component should end up having a unique current flowing through it. Like this:

For convenience I chose to number the currents to correspond to the resistor number in the branch (the exception is the current I₁ that flows through both R₁ and R₃ because they are in the same branch -- I picked the lower resistor number for the current number).

You could add a forth loop that traverses the outer perimeter of the circuit, but it is not necessary for solving the circuit: once you have every component "touched" at least once by some loop, you have enough loops.

Now you need to apply your KVL rules to write the equations. Do a "KVL walk" around each loop summing the potential changes due to voltage sources and the individual currents in the components. Then write KCL for each of the nodes. You'll find that you need to use one less node than you've identified (try it, you'll see why).

thank you very much..i some how understand it more now..but you see,the problem is we havnt been thought the KVL rule aswell...but to due to a research I made,i understand summing all the voltages =0>am I right

 

[Yosty22]

That's correct. The sum of the voltages in each loop must equal zero. The same goes for the sum of all of the currents at each junction. Does that make sense?

 

[gneill]

thank you very much..i some how understand it more now..but you see,the problem is we havnt been thought the KVL rule aswell...but to due to a research I made,i understand summing all the voltages =0>am I right

Yes. You want to sum all the potential changes as you "walk" around a loop. Think of it as walking a closed path on hilly terrain where you're keeping track of the changes in elevation.

For sources, if you "walk" through them from their - to + terminals the potential increases. If you "walk" through them from + to -, the potential decreases.

For resistors you use Ohm's law and the current assigned to that resistor. If you "walk" through the resistor in the same direction as the current, the potential drops by I*R. If you're walking against the direction of the current, the potential increases by I*R.

In this way you can add up the potential changes, writing an equation as you go.

 

[Simon Bridge]

The KVL rule is actually what you've been trying to do - probably not so formally.
Applied to loop 1, you get:

$V_1-I_1R_1-I_2R_2-I_1I_3=0$

...which is the same as:

$V_1=I_1R_1+I_2R_2+I_1I_3$

...which is close to your first equation, compare it with the examples in your classwork.

Have a look at:
http://www.ni.com/white-paper/14449/en/


Both these use 2-loop circuits as examples. That does not matter.
More loops will give you extra equations - the rules are applied in just the same way.

The rules also work for circuits of arbitrary shapes - like with loops that are triangles - and where the loops are jumbled together instead of being in a neat row like in your exercise. Therefore you will always get problems that don't look like your examples. Don't let that confuse you, it's an important part of your training: you are training to be able to solve problems nobody knows the answer to - maybe nobody has ever seen before.

It's fun :)