Problem 13-9    Source:   Problem developed by the site author.

For the circuit shown in Figure 13-09.1, knowing that V = 60 volts and using Kirchhoff's law, determine:

a) The voltage at the point A, that is, V_A.

b) The potential difference between the points c-e.

Solution of the using Ohm's Law   click here!

Solution of the Problem 13-9   -    Kirchhoff's Method

Item a

Using the voltage mesh method ( Kirchhoff's law ) we know that in a closed loop, the algebraic sum of the voltages must be equal to ZERO . Note that point A of the resistance of 80 Ω is not connected to anything. Therefore, the voltage at that point will be equal to the voltage at point a , as there will be no current flowing through this resistance. Therefore, we can eliminate this resistance from the circuit. On the other hand, the resistance of 40 Ω is in parallel with the voltage source and can also be eliminated from the circuit. In Figure 13-09.2 we see the circuit redesigned with a new topology for clarity.

In the figure above, we realize that we can simplify the circuit a little more in order to make it more easy to understand the calculation of the currents involved in solving the problem. So, using Kirchhoff's law and based on the circuit shown in Figure 13-09.3 we can determine the equations for the three loops in the circuit.

So we have a system of three equations to three unknowns, which can be solved by Crammer rule, by substitution, etc ... After the calculations we find the values of I_a, I_b and I_c.

Pay close attention that the calculated currents are valid for the circuit represented in Figure 13-09.3 . Now, we must find the relation between the calculated currents in this circuit and the currents shown in the circuit of Figure 13-09.2 . Then, comparing the two circuits we have:

I)The current I₁ = I_a - I_b.

II) The current I₂ = I_b.

III) and the current I₃ = I_b - I_c.

Then, performing the calculations, we found

Item b

To calculate the potential difference between points c-e , we must calculate the voltage at point c and at point e . So:

And by definition, we know that V_ce = V_c - V_e. Then