Determine currents Ia, Ib and Ic

[The Electrician]

Just to show how easy it can be.

Solving circuits usually ends up being a problem of solving a system of simultaneous equations. There is a way to write down a system of simultaneous equations that shows them in a very compact form. That way is to use matrix notation. Your two mesh equations can be shown in matrix form like this:

Solving simultaneous equations involves elimination of variables until a single equation in one unknown is obtained. That equation is solved for that unknown, and the result is then substituted in the remaining equations. Then another variable is solved for, and the process is continued until you have all the unknowns solved.

Once in this form, a linear solver can be used, which does all the elimination and back substitution for you, avoiding much mistake prone, tedious, algebra:

Here's how it looks on the HP50G calculator in matrix form:

And, after pressing one button, here's the solution:

It would be worth your while to learn how to do this. Don't forget the free software Scilab, but a handheld calculator is very convenient.

at the end it wasnt difficult but it took me almost two days to do that

You've had enough practice doing it by hand. Learn to use a mathematical software or calculator!

 

[agata78]

Yeap its correct, i got the same!
Ia= -0.0142-0.009jbut Ib

10-Ibj25 - Ia100
10- Ibj25- ((-1316-8400j)/ 92209 ) x j100
10- Ibj25- (- 131600j- 840000j2) / 92209
-Ibj25= (-131600j + 840000 / 92209 ) -10
-Ibj25= (-131600j+840000-922090)/ 92209
-Ibj25= (-131600j- 82090) / 92209
-Ibj25= -1.427j - 0.8902
Ib= (-1.427j - 0.8902) / (-25)

Ib= 0.057j + 0.0356j

Can you check my calculations please?

 

[The Electrician]

Yeap its correct, i got the same!
Ia= -0.0142-0.0911jbut Ib

10-Ibj25 - Ia100
10- Ibj25- ((-1316-8400j)/ 92209 ) x j100
10- Ibj25- (- 131600j- 840000j2) / 92209
-Ibj25= (-131600j + 840000 / 92209 ) -10
-Ibj25= (-131600j+840000-922090)/ 92209
-Ibj25= (-131600j- 82090) / 92209
-Ibj25= -1.427j - 0.8902
Ib= (-1.427j - 0.8902) / (-25j)

Ib= 0.057j + 0.0356j

Can you check my calculations please?

You left out a "j" in your last step.

Don't forget the numerical error involving -.0911 that gneill already mentioned.

See how easy it is to make a mistake? Just imagine trying to do this during an exam without making a single mistake!

 

[agata78]

Ib supposed to be= +0.0571 - 0.0356j.

mine is Ib= 0.057j + 0.0356j
Can you check my calculations:

10-Ibj25 - Ia100
10- Ibj25- ((-1316-8400j)/ 92209 ) x j100
10- Ibj25- (- 131600j- 840000j2) / 92209
-Ibj25= (-131600j + 840000 / 92209 ) -10
-Ibj25= (-131600j+840000-922090)/ 92209
-Ibj25= (-131600j- 82090) / 92209
-Ibj25= -1.427j - 0.8902
Ib= (-1.427j - 0.8902) / (-25j)

Ib= 0.057j + 0.0356j

 

[The Electrician]

Ib= (-1.427j - 0.8902) / (-25j)

Ib= 0.057j + 0.0356j

You've made some kind of error in this last step. The sign in front of the 0.0356 is in fact minus if you do the complex arithmetic correctly.

This kind of error won't happen if you use a calculator that can do complex arithmetic.

 

[agata78]

Ib= 0.057j + 0.0356

Still i need minus inside, i checked a few times and it is plus!

 

[gneill]

Ib supposed to be= +0.0571 - 0.0356j.

mine is Ib= 0.057j + 0.0356j
Can you check my calculations:

10-Ibj25 - Ia100
10- Ibj25- ((-1316-8400j)/ 92209 ) x j100
10- Ibj25- (- 131600j- 840000j2) / 92209
-Ibj25= (-131600j + 840000 / 92209 ) -10
-Ibj25= (-131600j+840000-922090)/ 92209
-Ibj25= (-131600j- 82090) / 92209
-Ibj25= -1.427j - 0.8902
Ib= (-1.427j - 0.8902) / (-25j) <---- at this point, multiply top and bottom by +j. What do you get?

Ib= 0.057j + 0.0356j

You've got a sign issue occurring in whatever steps you take between the line indicated above and your final line.

 

[agata78]

but i don't understand why i have to multiply by +j

minus divide minus is plus
and i divide -25 both sides

 

[agata78]

I did multiply top and bottom by +J.

Ib= 0.057- 0.0356j

 

[gneill]

but i don't understand why i have to multiply by +j

minus divide minus is plus
and i divide -25 both sides

You want to clear the j from the bottom. So multiply top and bottom by j. Try it.

 

[agata78]

I did and it works.
The answer is :

Ib= 0.057- 0.0356j

 

[gneill]

I did and it works.
The answer is :

Ib= 0.057- 0.0356j

Okay!

So you'll have to analyze the logic of whatever method you used before in order to spot where the sign got lost.

 

[agata78]

Thank you! Two more to go!