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.

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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