Solve Simultaneous Equations: Loop/Junction Eqns

[viv12345]

Homework Statement

Need help setting up the equations to solve for the unknowns. I get the general idea but not sure how to begin actually solving the problem

Relevant Equations

+1.56 - 43i1 - 75i2 = 0
+1.6 - 100i3 - 75i2 = 0
+i1 - i2 + i3 = 0——-> i1 + i3 = i2

+1.56 - 43i1 - 75i2 = 0
+1.6 - 100i3 - 75i2 = 0
+i1 - i2 + i3 = 0——-> i1 + i3 = i2

 

[haruspex]

The standard way to solve simultaneous equations is to get one of them into the form (unknown a)=(some function of the other remaining unknowns)
Then use that to replace unknown a in all of the remaining equations .
You now have a system with one fewer unknowns and one fewer equations. Repeat the process.

 

[DaveE]

Um... What?

Need help setting up the equations to solve for the unknowns.

It looks like you've already done that. But you won't get useful help from us if we don't know the problem your trying to solve.

I get the general idea but not sure how to begin actually solving the problem

Are you asking how to solve this system of 3 equations and 3 unknowns?

 

[viv12345]

Are you asking how to solve this system of 3 equations and 3 unknowns?

Yea, so I need to solve for i1, i2, and i3. I simplified the first equation to 1.56-118i1-75i3=0 from 1.56-43i1-75(i1+i3)=0 and did the same for the second equation but I don't know where to go from there. I'm just trying to follow what my professor did but after simplifying the equations, he picked a random number with no explanation to solve the equation so I'm really confused.

 

[haruspex]

Yea, so I need to solve for i1, i2, and i3. I simplified the first equation to 1.56-118i1-75i3=0 from 1.56-43i1-75(i1+i3)=0 and did the same for the second equation but I don't know where to go from there. I'm just trying to follow what my professor did but after simplifying the equations, he picked a random number with no explanation to solve the equation so I'm really confused.

Have you tried the method I described in post 2?

 

[Hill]

OK, you got an equation with two unknowns, i1 and i3. If you subtract your second equation from the first, you get another equation with the same two unknowns. This way, you reduce the three equations with three unknowns down to two equations with two unknowns. Can you continue and reduce them to one equation with one unknown?

 

[haruspex]

OK, you got an equation with two unknowns, i1 and i3. If you subtract your second equation from the first, you get another equation with the same two unknowns.

Although that works, @viv12345 needs to learn the general method.

 

[Hill]

Although that works, @viv12345 needs to learn the general method.

Right. They also need to know that there often is more than one way to solve a problem.