DC Electrics - Basic Principles — Page 10, Lesson 19

I want to walk you through the basic principles of DC Electrics, starting with the three key power formulas you'll use constantly as a professional pilot. We begin with two fundamental relationships: Ohm's Law, which states that voltage equals current times resistance, written as V equals I times R, and the power formula, which says power in watts equals voltage times current, written as W equals V times I. From these two, we can derive three different ways to calculate power, depending on which quantity is unknown. If voltage is unknown, we use W equals I squared times R. If resistance is unknown, we use W equals V times I — that's the original formula. If current is unknown, we use W equals V squared divided by R. Now, here's a critical practical point: when a current passes through a resistor, that resistor becomes hot. If the current becomes excessive, the resistor will eventually melt. The amount of heat developed by a current I in a resistor R is I squared R watts. Notice that the heating effect is proportional to the square of the current. That means a small increase in current causes a significant increase in heating effect — this is why current limits are so important. Every electrical component is given a power rating, which is the maximum wattage it can handle. If that rating is exceeded, the component will overheat. A common example is a 60-watt light bulb — exceed that wattage and it fails. In an aircraft, each electrical circuit is protected by a fuse or a circuit breaker. These devices prevent the maximum power rating of a component from being exceeded by breaking the circuit if the current increases too much. Let's move on to series and parallel circuits. More than one resistance can be connected in any one circuit, and they can be connected in two ways: in series, meaning one after the other, or in parallel, meaning alongside each other. Starting with series circuits. A series connection reduces current flow and therefore reduces power consumption. However, it can be impractical because individual loads, which are the resistances, cannot be individually controlled. Also, if one resistance fails, the entire circuit fails — that's a major drawback. The total circuit resistance in a series circuit is calculated by simply summing the individual resistances. The formula is R subscript T equals R1 plus R2 plus R3. For example, if R1 is 4 ohms, R2 is 6 ohms, and R3 is 10 ohms, then R subscript T equals 4 plus 6 plus 10, which gives 20 ohms. Using Ohm's Law, V equals I times R, so current equals voltage divided by resistance. With a 12-volt supply and 20 ohms total resistance, the current is 12 divided by 20, which equals 0.6 amps. Now let's look at parallel circuits. A parallel connection ensures each resistor is individually controllable and receives the same voltage. Failure of one resistor will not affect the others — this is a huge advantage. Most aircraft loads are connected in parallel for exactly this reason. The total circuit resistance in a parallel circuit is found using a different method. The formula is 1 over R subscript T equals 1 over R1 plus 1 over R2 plus 1 over R3. Using the same resistor values — 4, 6, and 10 ohms — we get 1 over R subscript T equals 1 over 4 plus 1 over 6 plus 1 over 10. Finding a common denominator of 60, that becomes 15 over 60 plus 10 over 60 plus 6 over 60, which equals 31 over 60. So 1 over R subscript T equals 31 over 60, meaning R subscript T equals 60 over 31, which is approximately 1.94 ohms. With a 12-volt supply, current equals 12 divided by 1.94, which gives about 6 amps. Notice how much lower the total resistance is in parallel compared to series — and how much higher the current is. Finally, we have combination circuits that include both series and parallel resistors. The method is to first evaluate the parallel resistors, then add that result to the series resistor. For example, if you have a 10-ohm and a 6-ohm resistor in parallel, with a series resistor elsewhere, you start with the parallel pair. Using 1 over R subscript T equals 1 over 10 plus 1 over 6, the lowest common denominator is 30, giving 3 over 30 plus 5 over 30 equals 8 over 30. So 1 over R subscript T equals 8 over 30, meaning R subscript T for the parallel pair is 30 over 8, which equals 3.75 ohms. Then you add that to the series resistor to get the total circuit resistance. There's also an alternative method specifically for calculating the resistance of two resistors in parallel. The formula is R subscript T equals R1 times R2 divided by R1 plus R2. Using the same example, 10 times 6 is 60, divided by 10 plus 6 which is 16, gives 60 over 16, which is 3.75 ohms — the same result. This is often quicker when you only have two resistors in parallel.