Lightning bolt vs. batteries: a coulomb in everyday terms

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).

Probably right, keep energy and charge apart ( mentally ) they measure different things.

Your instinct was right. The article is misleading.

The article ignored voltage. If you use the Hydraulic Analogy, voltage is like the temperature/pressure of the water. Essentially, the water from the battery has an extremely low temperature/pressure. The temperature/pressure of the water from the lightning, however, is HUGE. Basically, there is WAY MORE TOTAL ENERGY (Joules) in the lightning than in the battery. This is measured in Joules (kg.m/s^2).

Let's compare the TOTAL ENERGY of the lightning and the battery.

$$Volts = \frac{Joules}{Coulombs}$$

Lightning:

15 Coulombs

500 million Volts

15C x 500000000V = 7.5 Billion Joules (kg.m/s^2)

AA Battery:

5000 Coulombs

1.5 Volts

5000C x 1.5V = 7,500 Joules (kg.m/s^2)

There's a million times more energy in a bolt of lightning than in an AA battery.

Why the confusion? The battery sends vastly more electrons through the wires (5000 Coulombs), but those electrons have almost no energy in them. By comparison, the lightning sends a very small number of electrons (15 Coulombs) but those few electrons still carry vastly more total energy.