# Is it possible to calculate the energy of a spark?

I am not a physicist, but this question came to me and I need to answer it, and I think that you guys can help me.

Is it possible to calculate the energy in a spark? For example in a lighter with an 'electric ignition'.

If it is, how can I do that?

• Do you mean a lighter with an 'electric ignition' type spark or the old-school 'flint-stone' types (eg: 'Zippo') ? – theo Jan 15 '15 at 1:21
• @theo I mean the first one, the lighter with an 'electric ignition'. Thanks for comment – fdofuenzalida Jan 15 '15 at 3:47
• Well then it should be easy enough to measure the energy if we know (can measure) the voltage and current as functions of time, since energy is given by $E=\int_0^t \! v(t)i(t) \, \mathrm{d}t$ – theo Jan 15 '15 at 4:57

One way is to connect the ignition to a high voltage (10kV) capacitor. Then the energy is: $$E = \int VI d t = \frac{CV^2}{2},$$ where $C$ is its capacitance and $V$ its voltage, assuming that you connected it and did the measurements so that energy losses are negligible.

When you create a spark you generate a voltage, $V$, between the two electrodes and a current, $I$, flows between them. Both the voltage and the current vary with time, so we need to write them as functions of time: $V(t)$ and $I(t)$.

If we have a current $I$ flowing across a voltage $V$, then the power is given by:

$$W = VI$$

Energy is power multiplied by time. So if we take a very short time $dt$ the energy in that time is:

$$dE = VIdt$$

Now, in our system (the spark) both the voltage and current are functions of time, so to calculate the total energy we need to integrate $VIdt$:

$$E = \int V(t) I(t) dt$$

And that's how we calculate the total energy in the spark.

But ...

Whether this answers your question or not I don't know, because I haven't actually calculated the energy. That's because I don't know how the voltage and current vary with time. How $V(t)$ and $I(t)$ vary with time will depend on the exact details of the spark. Obviously a gas lighter is going to be very different to a lightning bolt. There isn't an general rule to say how the voltageand current will vary with time so I can't provide a general answer. To actually calculate the energy in a spark would require detailed knowledge about the specific system you were considering.