Solving equations simultaneously circuits

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SUMMARY

This discussion focuses on solving simultaneous equations in electrical circuits, specifically for the variable i1. The equations provided are E - i1 - Ri2 = 0, Ri2 - Ri3 = 0, and i1 + i2 + i3 = 0, where all resistances (R) are equal to 0.73 x 10^6 ohms. The solution involves rewriting the equations to isolate currents and substituting values to eliminate variables, ultimately leading to a simplified system of equations. The key takeaway is the importance of substitution and simplification in solving for unknown variables in circuit equations.

PREREQUISITES
  • Understanding of Ohm's Law and circuit analysis
  • Familiarity with simultaneous equations
  • Basic knowledge of electrical components and their relationships
  • Ability to manipulate algebraic expressions
NEXT STEPS
  • Study techniques for solving simultaneous equations in electrical circuits
  • Learn about Kirchhoff's laws and their application in circuit analysis
  • Explore the use of matrix methods for solving systems of equations
  • Investigate the impact of varying resistance values on circuit behavior
USEFUL FOR

Electrical engineers, physics students, and anyone involved in circuit design or analysis will benefit from this discussion, particularly those looking to improve their skills in solving complex circuit equations.

spottedcow913
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I really struggle with these and would just like someones input on how to best solve these, I can never seem to cancel everything out except the variable I am looking for. I have:

E-i1-Ri2=0
Ri2-Ri3=0
i1+i2+i3

I am looking to solve for i1

All R's are equal to 0.73 x10^6 ohms so I just simplified them all to R instead of R1 R2 and R3
 
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Your first equation seems to be wrong because the units don't work out. I'll assume there's supposed to be an R before i1.

I'd start by rewriting them slightly so it's easier to see what to do:

Code:
R i1 + R i2        = E
       R i2 - R i3 = 0
  i1 +   i2 +   i3 = 0

Divide the first and second equations by R so all you have are currents on the left.

Code:
i1 + i2      = E/R
     i2 - i3 = 0
i1 + i2 + i3 = 0

Can you see how you can get rid of i3 and end up with two equations involving just i1 and i2?
 
hi spottedcow913! :smile:

(try using the X2 icon just above the Reply box :wink:)

just solve the equations one at a time

in this case, start with the middle one, and you get I2 = I3

now substitue that into the third one …

what do you get? :smile:
 

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