Solve Simultaneous Equations: Loop/Junction Eqns

In summary, the conversation involves a person seeking help with solving a system of three equations and three unknowns. They have simplified the equations but are unsure of how to proceed with solving them. Another person suggests a method of reducing the number of unknowns by subtracting one equation from the other, and emphasizes the importance of learning the general method for solving equations.
  • #1
viv12345
2
0
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
 
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  • #2
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.
 
  • #3
Um... What?
viv12345 said:
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.

viv12345 said:
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?
 
  • #4
DaveE said:
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.
 
  • #5
viv12345 said:
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?
 
  • #6
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?
 
  • #7
Hill said:
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.
 
  • Like
Likes DaveE
  • #8
haruspex said:
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.
 

1. What is a simultaneous equation?

A simultaneous equation is a set of two or more equations that contain two or more unknown variables. The goal is to find the values of the variables that satisfy all of the equations at the same time.

2. What is the difference between loop and junction equations?

Loop equations involve a closed path in a circuit, while junction equations involve the flow of current into and out of a junction point. Loop equations are used to solve for unknown voltages, while junction equations are used to solve for unknown currents.

3. How do you solve simultaneous equations using loop equations?

To solve simultaneous equations using loop equations, you first label the unknown voltages in the circuit. Then, you write loop equations for each closed path in the circuit, using Kirchhoff's voltage law. Finally, you solve the resulting system of equations to find the values of the unknown voltages.

4. How do you solve simultaneous equations using junction equations?

To solve simultaneous equations using junction equations, you first label the unknown currents in the circuit. Then, you write junction equations for each junction point in the circuit, using Kirchhoff's current law. Finally, you solve the resulting system of equations to find the values of the unknown currents.

5. What are some tips for solving simultaneous equations?

Some tips for solving simultaneous equations include: identifying the type of equations (loop or junction), labeling the unknown variables, writing the equations accurately, using the correct laws (Kirchhoff's voltage law for loop equations and Kirchhoff's current law for junction equations), and solving the system of equations using methods such as substitution or elimination.

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