Using Kirchhoff's Laws to find current in a circuit

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SUMMARY

This discussion focuses on applying Kirchhoff's Laws to determine the currents I1, I2, and I3 in a given electrical circuit. The user has derived two equations from the circuit analysis: I2 = I1 + I3 and two loop equations resulting in 1V - (1 ohm)I1 - (2 ohms)I2 = 0 for the left loop and 1V - (1 ohm)I3 - (1 ohm)I2 = 0 for the right loop. The user is struggling to solve the system of equations due to terms canceling out, leading to incorrect conclusions about the current values. Assistance is requested to resolve the equations accurately.

PREREQUISITES
  • Understanding of Kirchhoff's Voltage Law (KVL)
  • Familiarity with Kirchhoff's Junction Law (KCL)
  • Basic knowledge of circuit analysis techniques
  • Ability to solve systems of linear equations
NEXT STEPS
  • Review techniques for solving systems of equations, particularly substitution and elimination methods.
  • Study examples of applying Kirchhoff's Laws in complex circuits.
  • Learn about nodal analysis as an alternative method for circuit analysis.
  • Explore the use of simulation tools like LTspice for circuit verification.
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Students studying electrical engineering, physics enthusiasts, and anyone looking to deepen their understanding of circuit analysis using Kirchhoff's Laws.

klandestine
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I have attached a picture of a circuit. I am trying to find the values of I1, I2, and I3. What I have come up with so far, using Kirchhoff's Voltage and Junction Laws is:
I2=I1+I3
for the left loop:
9V - (5 ohms)I1 -4V - (10 ohms)I2 = 0
which simplifies to:
1V - (1 ohm)I1 - (2 ohms)I2 = 0
for the right loop:
14V - (10 ohms)I3 -4V - (10 ohms)I2 = 0
which simplifies to:
1V - (1 ohm)I3 - (1 ohm)I2 = 0
I am pretty certain that I have these correct, but I can't seem to solve my system of equations--whenever I try to add or subtract the equations, several terms cancel, leaving me with a current equaling zero.
I would really appreciate some help. Thank you. :!)
 

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