Power output of ignition coil

I have a 12V battery connected to a circuit driving an ignition coil. The circuit requires 2A to run. The ignition coil produces 40,000V and the spark is measured at 50mA. By simple calculations the input power is 24W the output power is 2000W, how?

If I could harness the output power and my battery is 200Wh does this mean I can run a 2000W device for 8.3 hours, as the input is only 24W from the battery?

This does not seem right, what am I missing?

Or am I actually drawing 2000W power from the battery (over time) to charge the capacitors in the circuit etc, meaning that it will only last 6 minutes?

Thanks for the help.

Answer

You need to read up on spark ignition systems and could perhaps start with something like this.

You are correct in thinking that the output power is in kW, but unfortunately you left out an important element ...time. Spark gap time is in the 1 - 2 ms range for most systems depending on inductor values and total series resistance for the circuit.

Most Kettering systems have input currents in the 10 - 20 A range (I've not seen current in the 2 A range) at 12 V and produce about 40 kV in the secondary.

The currents that flow in the secondary (in the spark gap) can also very high (in the hundreds of mA). Initial breakover currents are typically in the 3 - 5 mA range, and increase to the 100 - 200 mA range as the gap voltage rapidly decreases.

In older systems with long spark plug leads the lead resistance may be several 10's kOhms and along with the higher resistance of the secondary coils this limits the current that will flow. With these systems spark line current may be design limited (by the series resistance) to 200 - 500 mA.

The power dissipated in the spark gap is limited both in time and voltage/current. At breakover (zero current) the voltage at the gap will rapidly rise to 40 kV, but once the plasma is created the instantaneous voltage will drop to only a few hundred volts. In older systems with a distributor gap, you had to create two plasma connections, one for the distributer and one in the cylinder spark plug. Losses abounded.

Modern systems typically use a coil-on-plug design which get's rid of one of the spark gaps (double the delivered spark energy), reduces series resistance and increases the plasma current (much 'hotter' sparks). Spark line current in these is still limited by design, typically to under 200 mA.

Read the document I linked to, it'll give you a good idea on modern systems.