Electrical – Kirchhoff’s Law and Superposition Theorem

kirchhoffs-lawssuperpositionvoltage

For the given circuit I found the current and the voltage at R1, R2, R3, using the superposition theorem.
1.I replaced the VS2 with a short then calculated:
I1= 0.57mA, I2=0.33mA, I3=0.2mA, V1= 2.68V, V2=2.02V, V3=2.97V.
2. Then I replaced the VS1 with a short and then calculated:
I1=-0.99mA, I2=-0.58mA, I3=0.4mA, V1=3.19V, V2=6.7V, V3=3.2V

So, the total current and voltage for each resistor is :
I1=0.26mA, I2=-0.65mA, I3=0.91mA
V1= 5.86V, V2=9.16V, V3=5.5V

I have to prove the Kirchhoff’s voltage and current Law are valid in the circuit given.
Can someone help me with this?

circuit

Best Answer

schematic

simulate this circuit – Schematic created using CircuitLab

First of all, mark all currents on all branches with their magnitude and direction as you calculated.

To verify Kirchoff's current law:

  • For node E, consider currents entering and leaving the node - \$I_{R1}, I_{R2}, I_{R3} \$

  • Similarly for node G, consider currents - \$I_{R3}, I_{DG}, I_{GB} \$

  • Prove that the algebraic sum of currents leaving the node = algebraic sum of currents entering the node.

To verify Kirchoff's voltage law:

  • Consider all 3 loops in the circuit - AEGB, ECDG, ACDB.

  • Prove that the sum of all voltage drops and voltage sources = 0 in each loop.

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