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.
 

FAQ: Solve Simultaneous Equations: Loop/Junction Eqns

What are simultaneous equations in the context of loop/junction equations?

Simultaneous equations in the context of loop/junction equations refer to a set of equations that describe the current and voltage relationships in electrical circuits. These equations are derived from Kirchhoff's laws: Kirchhoff's Current Law (KCL) for junctions and Kirchhoff's Voltage Law (KVL) for loops. Solving these equations simultaneously allows us to find the unknown currents and voltages in the circuit.

How do Kirchhoff's laws apply to solving simultaneous equations in circuits?

Kirchhoff's Current Law (KCL) states that the total current entering a junction must equal the total current leaving the junction. Kirchhoff's Voltage Law (KVL) states that the sum of all voltages around a closed loop must equal zero. These laws provide the necessary equations that describe the behavior of electrical circuits. By applying these laws to different loops and junctions in a circuit, we can set up a system of simultaneous equations that can be solved to determine unknown quantities.

What methods can be used to solve simultaneous equations in loop/junction problems?

Several methods can be used to solve simultaneous equations in loop/junction problems, including substitution, elimination, and matrix methods (such as Gaussian elimination or using the inverse of a matrix). For larger systems of equations, computational tools like MATLAB or specialized circuit simulation software can be employed to solve the equations efficiently.

Can you provide a simple example of solving simultaneous equations for a circuit?

Consider a simple circuit with two loops and one junction. Suppose we have the following equations from KVL and KCL:Loop 1: \( V_1 - I_1R_1 - I_2R_2 = 0 \)Loop 2: \( V_2 - I_2R_2 - I_3R_3 = 0 \)Junction: \( I_1 = I_2 + I_3 \)To solve these, we can use substitution or matrix methods to find the values of \( I_1 \), \( I_2 \), and \( I_3 \). For example, substituting \( I_1 \) from the junction equation into the loop equations allows us to solve for \( I_2 \) and \( I_3 \), and then back-substitute to find \( I_1 \).

What are common pitfalls when solving simultaneous equations in circuits?

Common pitfalls include incorrect application of Kirchhoff's laws, sign errors when summing voltages or currents, and arithmetic mistakes when solving the equations. Additionally, failing to account for all elements in a loop or junction, such as missing a voltage source or resistor, can lead to incorrect solutions. Careful setup and double-check

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