Problem 13-1    Source:   Problem elaborated by the author of the site.

For the circuit shown in the Figure 13-01.1, calculate:

a) The currents i₁, i₂ and i₃.

b) The voltage of the node e₁.

Solution of the problem using Method of Transforming Sources   Click here!

Solution of the problem using Nodal Voltage   Click here!

Solution of the problem using Superposition Method   Click here!

Solution of the problem using Thévenin/Norton   Click here!

Solution of the Problem 13-1   -    Kirchhoff Method

By the law of Kirchhoff for voltage, we know that in a closed loop the algebraic sum of the voltages must be equal to ZERO . In the figure above, we see the redesigned circuit where shows the currents i₁ and i₃. Note that, from the circuit seen in the figure above, we notice that the current i₂ that flows by the resistor of 2 ohms , is given by:

We can write the two equations for the two meshes of the circuit. Owing to the clockwise direction of the current we have:

Rearranging the terms, we arrive at:

Therefore, we have a system of two equations with two unknowns. After calculations, we find the values of i₁ and i₃.

Knowing the values of i₁ and i₃, we can find the value of i₂, or:

In this way, we can already calculate the value of e₁, or:

So the answer to the problem is:

If we want proof that these results are correct, we can take stock circuit power as shown Here!