Circuit Analysis 2:
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 2
Circuit Analysis Using KCL and KVL and 3 Simultaneous Linear Equations

Application of three simultaneous linear equations

Solve for I1, I2, and I3

Remember this is manual calculation with assumption that the circulating current I₁ and I₂ are both rotating in clockwise direction. In actual software simulation (LTSpice IV - Linear Technology, Simulation Program with Integrated Circuit Emphasize, owned by Analog Device, Inc.), you might get negative value answer the explanation is the current flow assumption.

Can you spot the AI hallucination on the above drawing? KVL - Loop 2 , - I₃I₂ that is not a voltage drop.

I₁ =

I₂ =

I₃ =

A solved problem becomes trusted automation—saving time and accelerating decision-making.

Try changing the value of input. You will get automatic answer in blue button.

Read below the manual calculation. Automated Intelligence is another meaning of AI. This becomes possible because of internet, cloud technology, 5G communication, and fast microprocessor.

Enter your new input data in the input box above diagram.

I1 + I2 + I3 = Equation 1 is derived using KCL at intersection node A of current I₁ , I₂, and I₃

Substitute the answer for I1, I2, I3 in equation 1, it should be very close to zero (0).
It means the answers are all correct.

I1 + I2 + I3 = Equation 2 is derived after simplified calculation of loop 1 using KVL. Here you are going to use the voltage drop created by I₂ multiplied by resistor value of 10 ohms for KVL summation.

Substitute the answer for I1, I2, I3 in equation 2, it should be very close to
It means the answers are all correct.

I1 + I2 + I3 = Equation 3 is derived after simplified calculation of loop 2 using KVL

Substitute the answer for I1, I2, I3 in equation 2, it should be very close to
It means the answers are all correct.

Default Answer:

Once you enter new input, the new answer will be displayed in blue button.

Answer, I1 = -1.698

Answer, I2 = 5.774

Answer, I3 = 4.075

The negative current for I₁ means, the actual current is flowing in opposite direction of the assumed current direction. The assumed current direction is clockwise rotation both for loop 1 and loop 2.

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.

R1 = 5 R2 = 10

R3 = 10 R4 = 4

R5 = 30

V1 = 30 V2 = 120

V3 = 60

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 current I₁ , I₂, and I₃ to equation 1, 2, and 3 to check if they are valid answer.

To validate your answer substitute the values of current I₁ , I₂, and I₃ 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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