Back in 1827, Georg Ohm described the relationship between voltage, current, and resistance in an electrical circuit—demonstrating that voltage and current varied in direct proportion to each other. This was codified in Ohm’s Law:

In the equation R stands for resistance (measured, predictably, in ohms), V for voltage (measured in volts, which take their name from the foppish inventor of the electric cell—early forerunner of those AA batteries—Count Alessandro Volta) and I for current (measured in amperes). Since an amp is a very large amount of current—most houses run on 10 amp supplies, and less than an amp can stop the heart—you’ll usually see current measured in milliamperes (mA), which are 1/1000 of an amp.

Electricity is almost invariably described with water analogies, so: Imagine a building whose water is supplied by a water tower. The supply of water in that tower is the voltage, the water flow is the current, and the diameter of the pipes determines the resistance. Since the pipes aren’t going to change, then it stands to reason that, as the water drains out of the tower, the water pressure will go down. Make up some arbitrary numbers, and you’ll see that holds in the formula: If R is fixed, then as V decreases, so does I. Similarly, if you replace all the plumbing with narrower pipes, you’ll have less water flowing to the taps, lower pressure, and will drain the tank more slowly.

To model the LED circuits in the Switchbox, you need to rearrange Ohm’s Law, breaking the voltage into two components:

V_S is the voltage of the power supply (the batteries), and V_L is the forward voltage the LEDs require. You can usually assume that an LED draws around 20 mA (0.02 amps)—but check the package or data sheet for your LEDs to be sure. Plug in the numbers for the circuit you built in Step 5, and you’ll find:

Ideally, you’d want to buffer the LED with a 50 ohm resistor or larger. 50 ohm resistors are rare, but 47 ohm resistors are ultra-common; the difference between the two is basically within the margin of error for the components. As you add each additional LED wired in parallel, you load another 0.02 amps of current draw to the circuit; hypothetically, you could make the second circuit in Figure 2-5 with a 25 ohm resistor.

If you’d rather use blue or white LEDs, which usually have a forward voltage near 4 volts, then you’d need to use a bigger power supply, such as a 9-volt battery. To make the first circuit in Figure 2-5 with a blue LED and 9 volts:

250 ohm resistors aren’t commonly manufactured, but 240 and 270 are. Although the 240 is within the tolerance and probably fine, be safe and go with the 270 (marked with red-violet-brown stripes), since a 9-volt battery can make a pretty impressive burn and blue LEDs can be pricey.

For a more complete discussion of electrical components, thumb to the appendix.