Application of KVL and KCL and
3 Simultaneous Linear Equations
by Apolinario "Sam" Ortega, founder IN-V-BAT-AI
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Circuit Analysis 1
Circuit Analysis Using KCL and KVL and 3 Simultaneous Linear Equations
Solve for I1, I2, and I3
Try changing the value of input. You will get automatic answer in blue button.
Remember: In manual calculation, you assume the direction of current flow. If the current value is negative it only means the direction of actual current flow is reverse.
Using LTSpice IV simulation to check the mathematical solution. Make sure the battery polarity ( + / - ) connection is reflecting the
actual wiring connection of the circuit you are trying to analyze.
SPICE default current flow starts from positive + battery terminal through negative - terminal.
Because of factory automation, it is now easier to do the circuit output testing.
I 1 +
I 2
+
I 3
=
Equation 1 for KCL at node A
I 1 +
I 2
+
I 3 =
Equation 2 for KVL at loop 1
I 1 +
I 2
+
I 3
=
Equation 3 for KVL at loop 2
A solved problem becomes trusted automation—saving time and accelerating decision-making.
I2 negative current only means the actual current flow is opposite to the assumed current flow. Do simulation by changing the value of R1, R2, R3, V1 and V2. Then watch the predicted current. Using the expected current output reading is one way to troubleshoot if there is a resistor value problem.
Answer, I 1(R1) = 1.158
Answer, I 2(R2) = -0.421
Answer, I 3(R3) = 0.737
PRACTICE SIMULATION: if you are troubleshooting the same circuit. Then you can update new values and check the expected values. if your actual test reading does not match the expected values then one of the components is defective. Today, you replace the whole circuit board if the expected output is no longer valid.
R1 = 2
R3 = 5
R2 = 4
V1 = 6
V2 = 2
Update any values of R1, R2, R3, V1, and V2 for troubleshooting. The equation will be updated for new data entry.
These are solved using Cramer's Rule; Keep in mind that sometimes Cramer's Rule doesn't work. Therefore always substitute the value of I 1, I 2, and I 3 to equation 1, 2, and 3 to check if they are valid answer.
To validate your answer substitute the values of I 1, I 2, and I 3 to your original equation 1 , equation 2, and equation 3. The answer must satisfy all the equations or the three specified constraint with very small error.
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Unique visitors as of 9/25/2026 = 242,208
from 141 countries