In analyzing circuits, whether it is simple or fairly complex, it’s noteworthy that there aren’t just a single or fixed way of analyzing them; over the years, engineers and physicists have devised ways to make analysis a lot simpler. These analyses are made possible by the most basic concepts—Ohm’s law in particular, finding the equivalent resistance of a circuit, and the concepts of current and voltage in series and parallel connections.

Kirchhoff’s voltage law or KVL, and Kirchhoff’s current law or KCL, prove to be indispensable laws in circuit analysis—more advanced topics almost make these laws a prerequisite knowledge. Kirchhoff’s voltage law hinges on the principle of conservation of energy, and states that the sum of all voltages in a closed loop is equal to zero, or in another understanding, that the sum of all the voltage rise is equal to the sum of all the voltage drops across the circuit. KVL can be best applied to a series circuit, because equal current in each element implies that voltages across them are not equal.

Kirchhoff’s current law, however, utilizes the principle of conservation of electric charge and states that the sum of all the currents flowing through a node is equal to the sum of all the currents leaving the same node. As opposed to KVL, KCL are better applied to parallel circuits since we know that in parallel circuits, voltages across parallel elements are equal and therefore implying that the sum of the current flowing through each element is equal to the current that entered their common node.

Finally, we can conclude that for these conditions of their applications, Kirchhoff’s voltage law is also more applicable in closed-loop circuits analysis; in analyzing circuits by looking at their corresponding nodes or junctions, it would be wise to use Kirchhoff’s current law.

DISCUSSION

In the experiment, we studied another way of solving circuits—practically, there are many methods of analysis available for use—which would be the Kirchhoff’s circuit laws. These laws, the Kirchhoff’s voltage law and Kirchhoff’s current law, proves to be worthy of knowing not only because they make the usual series-parallel relationships combined with Ohm’s Law to find required parameters easier, but also because more advanced topics in electrical and electronics engineering are usually utilizing these laws.

For the first circuit in the experiment, we have three resistors connected in series with resistance values of 171 Ω, 200 Ω, and 240 Ω labelled as R1, R2, and R3 respectively and a source voltage of 120 V. It is imperative that we calculate the circuit’s equivalent or total resistance, and being in series, the equivalent resistance of the three resistors would just be their sum:

REQ=R1+R2+R3

As for the circuit current Is, we used Ohm’s law, dividing the source voltage by the equivalent resistance. In computing for the individual voltage drops across the resistors, again we used Ohm’s law: voltage

across each resistor is equal to the product of the circuit current and their resistance value. Since the resistors are in series, the flowing current through each resistor would be equal, and that is simply Is.

The second circuit is a series combination, R2 and R3’s parallel combination connected in series with R1. For easier analysis, we calculated for the parallel equivalent of 300 Ω and 600 Ω, which would be 200 Ω. This means that the equivalent resistance of R2 and R3 would now be seen as connected in series with R1, therefore the current flowing through them would just be the circuit current Is. But then, there would be another way of finding the voltage across R1 and the combination of R2 and R3; realizing that they are in series, the voltage divider principle can be used for this purpose. The values gathered from two different methods are very close enough.

The third circuit involves three resistors R1, R2, and R3 connected in parallel with the source. However, the equivalent resistance of these resistors would require a different way compared to finding the equivalent resistance of resistors connected in series—the equivalent resistance can be computed by the reciprocal of the sum of the reciprocal of the resistance values:

REQ=1

(R1−1+R2

−1+R3−1)

As per the characteristic of parallel circuits, the voltage across each resistor would be equal, therefore implying that the current flowing through each would not be equal, and the sum would be just equal to the circuit voltage. These currents can be solved using Ohm’s law, but there is another method available; if series circuits utilize the voltage divider principle, parallel circuits in turn use the current divider principle. Just like the previous circuits, values gathered from two different calculations are in agreement.

The last circuit is a parallel combination, R2 and R3 connected in series, and their branch connected in parallel with R1. Using the concepts we already grasped from the previous circuits, the equivalent resistance of R2 and R3 would have the same voltage drop with the voltage drop across R1, being connected in parallel. To calculate for the current across R1 and the series combination of R2 and R3, we established their relationship being in parallel, that is,

V T=V 1=V 2,3

V T=I 1R1=I 2R2

I 1=V T

R1; I 2,3=

V TR2,3

And then, we realized that the measured values and the computed values are in agreement, guaranteeing that analysis of circuits aren’t always limited to a single method.