INTRODUCTION TO ELECTRONICS: Kirchhoff’s Laws ( Part 2 )

The Loop Rule states that the sum of voltage ( V ) rises and drops around a closed loop must equal zero. This observation is an extension of the Law of Conservation of Energy which states that energy is neither created or destroyed, but it has the ability to change form. Furthermore, the direction that is traveled around a closed-loop system will determine whether the current ( I ) value will be positive or negative. A negative calculation of current will indicate that an incorrect direction-of-travel was chosen. We will now re-emphasize this point by examining the following closed-loop system:

This closed-loop diagram contains a 15 V source that is in series with a 1-ohm resistor, a 5 V source, and another 1-ohm resistor. Please note that conventional current flows from the positive anode to the negative cathode of simple batteries. This system is made complicated by the fact that both positive terminals face one another. Which direction will current flow within this circuit?

We may easily surmise that the 15 V source will have a proportionally stronger influence upon current flow than the 5 V source. If this hypothesis is correct, the circuit will function as if a single 10 V source provided 5 A of current across two 1-ohm resistors in series:

V – IR₁ – IR₂ = 0

R₁ = R₂

V = ( I )( 2R )

10 V = ( I )( 2 Ω )

I = 5 A

We will first move around the loop in a counterclockwise direction:

15 V – IR₁ – 5 V – IR₂ = 0

R₁ = R₂

15 V – 5 V – ( I )( 2R ) = 0

10 V = ( I )( 2R )

( 10 V / 2R ) = I

I = ( 10 V / 2 Ω ) = 5 A

Let us now traverse the same circuit in the clockwise direction:

– 15 V + IR₂ + 5 V + IR₁ = 0

   R₁ = R₂

– 15 V + ( I )( 2R ) + 5 V = 0

– 10 V + ( I )( 2R ) = 0

– 10 V = – ( I )( 2R )

– I = ( – 10 V / 2 Ω ) = – 5 A

Thus, the flow of positive charge in this single-loop circuit is in the counterclockwise direction; thus, when relatively complex multi-loop circuits are evaluated, a negative determination of current within any individual loop indicates that the direction of current goes in the opposite direction than was chosen.