In your motor car's engine (unless it runs on diesel) there will be one or occasionally more ignition coils. The job of the coil is to take a low voltage signal - from the points, or electronic ignition system, and turn it into high-tension to create a spark at the spark plugs, thereby igniting the fuel-air mixture.
A ballasted coil is a system employing a coil, resistor and relay to improve your chances when starting the car. It may seem a mysterious device at first, but it is really rather simple.
The voltage of a car, lets say it's based on 12 volts, may vary greatly during its use. While standing, the battery will put out around 12 volts. While the engine is running, and the alternator is spinning, we'll have 13 or more volts available. On starting, the power drawn by the starter motor will drop our potential to around 9 volts.
While the instruments in the car have a voltage regulator to ensure they work correctly whatever the voltage available, the ignition coil does not.
Traditionally, a coil would be designed to run at 12 volts, which seems a sensible choice. It can cope with being overpowered to a slight extent, so 13 volts will pose no problem. The real problem occurs when starting. As the starter motor is engaged, the power to the coil drops to 9 volts - and the spark becomes weak. Unfortunately, this is exactly the time we want a strong spark to get the engine going.
A ballasted coil system uses a coil designed to run at a lower voltage than the car's main systems. For example, we install a coil which only requires 9 volts in order to make a strong spark. Now - if we run this from 12 volts, we will burn it out quickly, so we add a resistor to drop the car's 12 volt system down to 9 volts for the coil.
The real beauty lies in the next part. As the starter-motor is engaged, we bypass the resistor using the relay. At this point, the power feeding the coil is our now-reduced 9 volts - but that's exactly what the coil requires. The spark is strong and the car starts first time.
When replacing the coil, you must always check whether you have a ballasted or non-ballasted system. Putting the wrong coil in will either produce a weak spark - if a non-ballasted coil is fitted to a ballasted car - or in the counter case, burn the coil out.
If you have a ballasted system, and forget to include the resistor, you will also burn the coil.