INTRODUCTION TO ELECTRONICS: Kirchhoff’s Laws ( Part 1 )

Conventional current ( I ) within an electrical circuit travels from a positively charged anode to a negatively charged cathode terminal:

In reality, electric field lines are what emerge from the positive terminal and terminate on the negative one; thus, negatively charged electrons actually flow in the opposite direction. Envisioning current as mobile positive charges makes Kirchhoff’s Law calculations relatively simple. Before explicitly seeing why this is the case, let’s first have a look at the concepts that make things work.

We first make note of the Law of Conservation of Energy. This law states that energy within a system cannot be created or destroyed, but it may change form. In order for a coulomb ( C ) of charge to lose energy as it traverses a circuit, it must have initially existed in some high-energy state. Assuming no losses, a +12 V source of conventional current will be -12 joules ( J ) less energetic once it arrives at the cathode. If we imagine this same current leaving its low-energy state by traveling through the 12 V source back to its high-energy state, its particles will gain 12 J of energy. This leads us to the first tenet of Kirchhoff’s Law:

1. The algebraic sum of the voltage rises and drops around a closed loop equals zero.

It is important to note that passage of current from a low to high-energy state back through the source is a figment of the imagination; no such event occurs, but this assumption about a closed-loop system is perfectly aligned with the laws of physics ( and very useful to us! ).

Let’s now revisit the closed-loop diagram above. The side of the resistor that is closest to the anode is positively polarized, and the side that is closest to the cathode is negatively polarized. As positive charges move from left-to-right from the anode, through the resistor, and to the cathode, they become more negative. The same charges become more positive as they complete the loop by passing back through the source. Herein lies the usefulness of positive currents of charge. By envisioning charges to first move “ upward “ through a source prior “ falling “ across the circuit’s resistor element, Kirchhoff’s Voltage Law becomes mathematically convenient:

V_rise – V_drop = 0

V_rise = V_drop

What would happen if we traveled the closed loop in the opposite direction? If we begin our journey at the anode, a voltage drop will occur as we move downward through the source. As we travel right-to-left through the resistor, a voltage rise will now occur. This circumstance would be evaluated as follows:

– V_drop + V_rise = 0

– V_drop = – V_rise 

It is important to note that resistance ( R ) values within electrical systems have a positive value:

V = IR

And,

– I_sourceR_source = – I_resistorR_resistor 

( – I_source )( R_source / R_resistor ) = – I_resistor

Even though our current value is now negative, nothing has changed about the energetic status of the system. When Kirchhoff’s Law is used to solve complex circuit problems, obtaining a negative value will indicate that the flow of current occurs in the direction that is opposite to the standard direction of travel.