DC Electrics - Basic Principles — Page 17, Lesson 21

I want to walk you through a key observation about parallel resistors, and then we’ll move into Kirchhoff’s Laws — two fundamental rules that govern how current and voltage behave in any electrical circuit. First, a note about total resistance when resistors are connected in parallel. The total resistance of resistors in parallel is always less than the value of the lowest resistor in that group. For example, if you have a 6 ohm resistor in parallel with some others, the combined resistance might come out to 3.75 ohms — which is indeed less than 6 ohms. That’s a useful check: if your calculation gives you a parallel total that’s higher than the smallest resistor, you’ve made a mistake. Now, if that parallel combination is then placed in series with another resistor, you add the series resistor to the parallel total to get the overall circuit resistance. So in the example given, the parallel group gives 3.75 ohms, and you add a 4 ohm series resistor, giving a total circuit resistance of 7.75 ohms. Let’s now turn to Kirchhoff’s Laws. There are two. Kirchhoff’s First Law says: The total current flowing into a point on a circuit is equal to the current flowing out of that point. In other words, charge doesn’t pile up at a junction — whatever current arrives must leave. If you have three wires meeting at a node, the sum of currents entering equals the sum of currents leaving. Kirchhoff’s Second Law says: If you add up all the voltage drops in a closed circuit, their sum always equals the voltage applied to that closed circuit. A closed circuit means a complete loop — current flows all the way around and returns to the source. The voltage applied is the battery or generator voltage pushing current around that loop. The voltage drops are the voltages used up across each component, like resistors, as current flows through them. Let’s prove the second law with a worked example. We have a simple series circuit with three resistors: 2 ohms, 4 ohms, and 6 ohms, all connected in series to a 12 volt supply. First, we need the total resistance. In series, you just add them up: RT = R1 + R2 + R3 RT = 2 + 4 + 6 RT = 12 ohms Now we use Ohm’s Law to find the current. Ohm’s Law says V = I × R, so rearranged, I = V ÷ R. The voltage applied is 12 volts, and the total resistance is 12 ohms: I = 12 ÷ 12 I = 1 amp So 1 amp flows through the entire series circuit. Now we can calculate the voltage drop across each resistor individually, again using Ohm’s Law V = I × R. Across the 2 ohm resistor: V = 1 amp × 2 ohms = 2 volts That means 12 volts enters the 2 ohm resistor, and 10 volts comes out the other side — 2 volts have been dropped. Across the 4 ohm resistor: V = 1 amp × 4 ohms = 4 volts 10 volts enters the 4 ohm resistor, and 6 volts exits. Across the 6 ohm resistor: V = 1 amp × 6 ohms = 6 volts 6 volts enters the 6 ohm resistor, and zero volts exit — all the remaining voltage is used up. Now add up all the voltage drops: 2 volts + 4 volts + 6 volts = 12 volts. That’s exactly the voltage applied to the circuit. This proves Kirchhoff’s Second Law: the sum of the voltage drops in a closed loop equals the applied voltage. So to summarise: Kirchhoff’s First Law deals with current at a junction — what goes in must come out. Kirchhoff’s Second Law deals with voltage around a closed loop — the drops add up to the supply. These two laws, together with Ohm’s Law, are the foundation for analysing any DC circuit you’ll encounter in aircraft electrical systems.