Twelve volts was a big deal when domestic manufacturers adopted it in the '50s. Doubling their voltage from 6 made electrical systems comparatively efficient and the increased power ushered in a new era of luxury and convenience.

Understanding that, what could possibly compel any of us to make a device that reduces the operating voltage in any part of our cars? Oh let us count the ways.

Because not everything in an early car can be converted to 12 V, the aftermarket offers convenient voltage drops. But convenience comes at a price: the cheap ones are notoriously inefficient and don't work on everything; the ones that will work on everything cost quite a bit of money. But we can build our own versions for a fraction of even the cheap ones. That's reason one.

Several automakers clung to 6V instruments for decades after they adopted 12V charging systems. Being mechanical, the voltage drops they employed eventually wear out. Replacements aren't cheap and being copies of the originals means they wear out too. But we can build solid-state versions that promise to last probably forever in automotive terms and for considerably less money. That's reason two.

Reason three is a result of new technology. Even the most technophobic among us rely on GPS to get around or listen to our MP3 players through our in-car radios. If you're one, you can bear testimony that their power supplies look bad and take up a lot of space.

That needn't be the case. Most of these devices rely on the Universal Serial Bus (USB) 5V standard so an oversized central power supply and USB ports wired into the car could replace all those warts-only you have to make them. And we can do just that for about the cost of a fast-food combo meal.

This and next month we'll show you how to address these issues. As most of us aren't electrical engineers, we stripped these tutorials to their bare essentials. In some cases all you have to do is copy the designs.

These solutions cost a fraction of what store-bought devices cost-provided they even exist. And let's face it, champagne taste on a beer budget is what motivates most of us. Think of it as hot rodding, geek style.

Resistors

The electrical version of a thumb pressed over the end of a garden hose, resistors restrict the amount of power that can pass through a circuit. While resistors still enjoy great popularity as current regulators for wiper and blower motors in cars swapped to 12 V, probably their greatest utility nowadays is in lighting.

We'll use LEDs for illustration because (a) they operate at little voltage, (b) they're useful as all hell, and (c) their current draw remains consistent. Consistency is especially important because we calculate a resistor's values upon the device's current draw.

Here's what a resistor looks like in real life and in schematic:

Resistor calculation relies on five elements:

• Vs or supply voltage is your car's voltage

• Vf or device voltage is the device's voltage rating

• I or device current is the rate of flow expressed in amperage

• R is the resistor's impedance expressed in ohms

• W is the resistor's power capacity expressed in watts

For our purposes let's say we want to use a 3.6V, 25mA resistor in a car that has a 12V charging system. That the system's voltage exceeds the LED's voltage means we have to choose a resistor to protect it.

First we must establish by just how much the circuit's voltage exceeds the device's voltage. To do that, we subtract the device's voltage (3.6) from the 13.6 V that a car's charging system produces (we call it 12 V but charging systems can nudge 14 V, so better to calculate for the maximum realistic voltage).

The voltage difference between 13.6 and 3.6 is 10. To determine how much impedance a resistor needs to prevent that extra 10 V from killing our LED we divide that figure by 0.025, the numeric expression of 25mA. A 400-ohm resistor would knock the extra 10 V from our 13.6V supply.

Easy, huh? We used a variant of Ohm's Law, the formula that we use to determine how electricity behaves. We just plugged our numbers into the following equation: R = (Vs - Vf) ÷ I

In this case R represents the impedance of our resistor; Vs represents our source voltage; Vf represents the device voltage; and I represents the device's current draw. As a reminder, always start with equations in brackets and work your way outward.

We also need to know our resistor's power capacity, or its wattage (W) rating. To solve for wattage we still subtract the device voltage from the supply voltage (Vs - Vf). Only instead of dividing that figure by the device's current rating (I) we multiply it. Our 10V difference multiplied by 0.025 (25mA) indicates 0.25 watts.

What we did was use another variant of Ohm's Law, only this time we solved for watts, not impedance. It looks like this: W = (Vs - Vf) x I

By the numbers we need a 400-ohm resistor with a 1/4-watt rating. Unfortunately it doesn't exist so we have to choose the resistor with the next greater impedance-in this case a common 470-ohm resistor. One with the next greater wattage is a good idea, in this case 1/2-watt.

So in the end, this is what our circuit looks like. You should recognize the resistor from before. The triangular job radiating arrows is the LED. More on that symbol later.

Resistors In Series Circuits

More than possible, it's actually favorable to use a resistor in a circuit with more than one device. Of the two ways we can do that, the most accessible way is in series.

When wired in series, the output from one device feeds another one's input. That second device either completes the circuit or feeds another device that in turn completes the circuit or feeds another device. And so on.

Here's what LEDs wired in series look like in schematic:

Series circuits are convenient because the voltage of the devices cumulates. Adding a second identical 3.6V LED to our earlier example would increase the device voltage to 7.2. The difference between 13.6 V and 7.2 is 6.4, which would require a less powerful resistor.

That's a good thing because resistors are sort of the enemy. As noted earlier, resistors dissipate power in the form of heat, which is waste to a lighting circuit. So instead of dissipating excessive energy as heat with resistors we can dissipate it as more light with LEDs. The circuit may still need a resistor, but it would be far smaller and waste less power.

The formula to calculate a resistor for devices wired in a series resembles the formulas to calculate a resistor for a single device. Only this time we combine the devices' operating voltages before we subtract that figure from our supply voltage. We then use the current load from just one LED, not both, to solve for the resistor's impedance and wattage. (That the formula references the current draw of just one device indicates something: the devices must maintain similar values.)

So if the LEDs were 25mA, we'd divide 6.4 (the surplus voltage) by 0.025 to determine the resistor's impedance; we'd multiply those two figures to determine the wattage. Rather than confuse things with the symbols, here's what the real numbers would look like in the formula (remember to work from the centermost brackets outward):

256 = [13.6 - (3.6 + 3.6)] ÷ 0.025

0.166 = [13.6 - (3.6 + 3.6)] x 0.025

So we'd need at least a 256-ohm, 0.166-watt resistor. The next larger would be a 270-ohm, 1/4-watt resistor.

More devices can be added to a circuit, but only to a point: the combined voltage of the components shouldn't exceed the supply voltage. Some maintain that the unregulated supply voltage must exceed the combined component voltage by at least a couple volts simply to accommodate the resistor. Case in point, three 3.6-volt resistors would amount to 10.8 volts, or about 2.8 volts. The tiny 120-ohm, 1/8-watt resistor necessary would hardly waste any power.

But not all devices lend themselves to series circuits. Many automotive devices are unique in the sense that they achieve ground through their mounting points (a blower motor, for example). Something like a motor can be part of series circuit, but only if it's the last device in the series. The problem is that the device that precedes the motor would have to have the same current draw and would have to feed the motor directly rather than grounding out on the body. Definitely impractical.

Resistors In Parallel Circuits

In introducing series circuits we indicated that there's a second way to use a resistor in a circuit with multiple devices. It's called parallel, and in it the path from a resistor splits into branches, each feeding its own device.

While it's a viable circuit, its application probably isn't appropriate for beginners. Among other things, if the devices aren't exact, the power takes the path of least resistance through the lesser-voltage device and leaves the others underpowered. Plus there aren't as many practical applications to use resistors on parallel circuits.

Where Resistors Don't Work

We've championed resistors as a means to control electricity but they don't work on everything. As noted before, resistors lend themselves to devices that maintain consistent current loads.

A car radio's current draws changes with its volume. The same goes for gauges: their needles' position depends upon current draw, which varies upon sender resistance. Resistors won't work for them because there's no set current that we can reference for calculations.

But not all is lost; we can build devices to drop the voltage for those applications too. In fact, we'll do just that next month.

Quick-Reference Formulas

Refer to the condensed versions of the formulas explained earlier. Simply replace the symbols with your circuit and device(s) figures to calculate resistance and wattage ratings.

To solve for resistor impedance*: R = (Vs - Vf) ÷ I

To solve for resistor wattage*: W = (Vs - Vf) x I

Legend

• Vs: Voltage Source

• Vf: Device Voltage

• I: Amperage

• R: Impedance expressed in ohms

• W Power expressed in watts

Combine device voltages to calculate series circuits but use current rating from only one device.

How to Read a Resistor

Colored bands printed on their bodies indicate most resistors' impedance values. The first two correspond with the first chart to indicate the base number-i.e. that orange is 3 and white is 9 indicates 39. The third band corresponds with the second chart to multiply or divide the base number.

A fourth band on most resistors indicates their ability to maintain impedance. Gold indicates a 5 percent tolerance; silver, 10 percent; and no band, 20 percent. Unfortunately there's no definitive indication of a resistor's wattage capacity.

BANDS 1 & 2 | BAND 3 | BAND 4 | |

Black | 0 | Black x 1 | Gold 5% |

Brown | 1 | Brown x 10 | Silver 10% |

Red | 2 | Red x 100 | None 20% |

Orange | 3 | Orange x 1,000 | |

Yellow | 4 | Yellow x 10,000 | |

Green | 5 | Green x 100,000 | |

Blue | 6 | Blue x 1,000,000 | |

Violet | 7 | Silver ÷ 100 | |

Gray | 8 | Gold ÷ 10 | |

White | 9 |