Electronic – Lightning bolt vs. batteries: a coulomb in everyday terms


I am trying to decide if the information on the wikipedia page


is reasonable. In particular the statements that a lightning bolt has about 15 coulomb, where a battery has 5000. My first instinct is that this is clearly wrong (a lightning bolt being such an energetic event, and a battery seeming mostly innocent), but then on reflection a lightning bolt does last only an extraordinarily short amount of time. In the end I am not sure how to check if this makes sense.

Best Answer

A common source of confusion is the difference between energy and power. A Snickers bar, for example, has more energy in it than a hand grenade. One might call a grenade exploding "energetic", but what's key here is its power (P), or ability to convert energy (E) extremely rapidly, in a very short amount of time (t):

$$P = \frac{E}{t}$$

Similarly, there is an analogy in the electrical world, where charge (Q), current (I), voltage (V), power and energy do not always go hand-in-hand.

The equations that relate all those are as follows:

$$ I = \frac{Q}{t} $$

$$ P = I{\cdot}V $$

$$ E = P{\cdot}t = I{\cdot}V{\cdot}t $$

$$ Q = I{\cdot}t $$

In the case of a lightning bolt, V and I are both extremely high, so the power is extreme, but t is fairly low, so the high current and short time mitigate each other somewhat, so there isn't an immense amount of charge. Of note, all that voltage influences is how much energy that the same amount of charge carries.

Plugging in some numbers, 120 kA & 30 µs, we get 3.6 coulombs, close to what you have. The Wikipedia article, however, says there is a fair bit of variability ("up to 350 C"), but they are within a couple orders of magnitude, and having seen a few lightning storms, some strikes are big and meaty, others not so much.

In a battery, the voltage is pathetic compared to a lighting strike, but that's irrelevant for calculating charge. What's key is that it's able to provide a current that's several orders of magnitude less for dozens of orders of magnitude longer. One milliamp for one hour (1 mA·h) is equal to 3.6 coulombs (look, the same as our 120 kA, 30 µs lighting strike), and batteries often have capacities in the thousands of mA·h (2000 mA·h is typical for an AA cell).

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