I have to find currents i1 and i3 in the following circuit using MESH ANALYSIS . I just wanted to know that if my EQUATIONS were correct. Thanks!

 

Have you confirmed that your proposed solution actually solves the original problem? That's the best way to check the correctness of your results. Of course, to do this it would be helpful to have all three mesh currents.

But it is good practice to verify your set-up equations before proceeding to solve them since all of the EE goes into the set-up equations and everything after that is math. If the set up equations are wrong, your math can be flawless and your answer will still be wrong (actually, will be simply be the right answer to a different problem).

There are a few ways to spot check your mesh equations. If you write them in the order of the terms, then they should be symmetric with the diagonal terms being positive and the off-diagonal terms being negative.

This allows you to write down the mesh equations by inspection. For each mesh, the coefficient for that current is the positive sum of all of the resistances around the mesh while for each of the other currents the coefficient is the negative of the sum of the resistances shared with that mesh. The right-hand side is the sum of the voltage gains going around the mesh due to the sources.

Also, if you add all of them together, you should get the loop equation going around the perimeter of the circuit.

 

Have you confirmed that your proposed solution actually solves the original problem? That's the best way to check the correctness of your results. Of course, to do this it would be helpful to have all three mesh currents.

But it is good practice to verify your set-up equations before proceeding to solve them since all of the EE goes into the set-up equations and everything after that is math. If the set up equations are wrong, your math can be flawless and your answer will still be wrong (actually, will be simply be the right answer to a different problem).

There are a few ways to spot check your mesh equations. If you write them in the order of the terms, then they should be symmetric with the diagonal terms being positive and the off-diagonal terms being negative.

This allows you to write down the mesh equations by inspection. For each mesh, the coefficient for that current is the positive sum of all of the resistances around the mesh while for each of the other currents the coefficient is the negative of the sum of the resistances shared with that mesh. The right-hand side is the sum of the voltage gains going around the mesh due to the sources.

Also, if you add all of them together, you should get the loop equation going around the perimeter of the circuit.

I just needed to verify a point here. For Example , lets see the 2nd mesh , both i2 and i3 are flowing through the 5ohms resistor , so we will include 5i2-5i3 in the equation( eq 2) of the Mesh Analysis of mesh #2 , instead of just 5i2. Am I right?

 

Your equation are right but your solution is wrong. So you did the electronics part right but the math part is wrong.

 

Your equation are right but your solution is wrong. So you did the electronics part right but the math part is wrong.

Thanks for verifying , I will see the maths part again.

 

Your equation are right but your solution is wrong. So you did the electronics part right but the math part is wrong.

Which underscores the need for:

Have you confirmed that your proposed solution actually solves the original problem? That's the best way to check the correctness of your results. Of course, to do this it would be helpful to have all three mesh currents.

 

I just needed to verify a point here. For Example , lets see the 2nd mesh , both i2 and i3 are flowing through the 5ohms resistor , so we will include 5i2-5i3 in the equation( eq 2) of the Mesh Analysis of mesh #2 , instead of just 5i2. Am I right?

Yes. Although you need to start properly tracking your units. You do not have the difference between two currents, but the difference between two voltages.

It needs to be (5 Ω)·i2 - (5 Ω)·i3.

 

Thanks for verifying , I will see the maths part again.

The point is that YOU need to be verifying your own solutions. You REALLY need to start doing that one EVERY problem you work. You will probably see your grades go up considerably and remember that in the real world you don't have someone to verify your results -- if that someone existed, they wouldn't need to be paying you.

 

The point is that YOU need to be verifying your own solutions. You REALLY need to start doing that one EVERY problem you work. You will probably see your grades go up considerably and remember that in the real world you don't have someone to verify your results -- if that someone existed, they wouldn't need to be paying you.

Thanks ! I was able to verify my currents and they satisfy the equations.

i1= 1086/41 A , i2= 1810/41 A , i3= 506/41 A

 

Thanks ! I was able to verify my currents and they satisfy the equations.

i1= 1086/41 A , i2= 1810/41 A , i3= 506/41 A

Good!

FWIW, I agree with your answers.