# Lightning bolt vs. batteries: a coulomb in everyday terms

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

http://en.wikipedia.org/wiki/Coulomb#In_everyday_terms

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.

• For more information see Physics for Future Presidents lectures (especially the first one) from Berkeley. There is lots of information about various forms of energy that will surprise even the engineers among us. – jpc Mar 21 '11 at 20:08
• @jpc, it seems your link broke. – Kortuk Feb 18 '12 at 8:41
• @Kortuk, URL rot, unfortunately. These lectures (including their "newer editions") can be found on the Berkeley channel on YouTube – jpc Feb 18 '12 at 14:48

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).

• -1 for not including at least 2 Maxwell equations. (+1) – tyblu Mar 1 '11 at 23:03
• Interesting... I liked the hand grenade analogy... Thanks. – BG100 Mar 1 '11 at 23:28
• I would still rather someone chuck me a Snickers bar than a grenade. – wilhil Mar 21 '11 at 19:36
• +1 if for the science and for the laughs I got from "A Snickers bar, has more energy in it than a hand grenade" and "In a battery, the voltage is pathetic" – Nicu Surdu Oct 9 '12 at 21:27
• Dozens of orders of magnitude longer than a microsecond would be a very long time. The minimum -2 dozen - is on the order of 100 billion hours? – C. Towne Springer Jun 2 '17 at 1:34

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

• BTW, the missing link is the voltage. A volt means that one coulomb carries one joule of energy. A battery operates at 12V, and lighting is in the tens of thousands or more ... – drxzcl Mar 1 '11 at 20:46
• Well, they're different but linked. Potential energy exists between charges. And the thousands of amps in a lightning strike is significant as well. It's just so brief that only a few coulombs gets transferred. – eryksun Mar 1 '11 at 23:44

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.

• $$P = \frac{E}{t}$$ There is way more total energy (Joules) in lightning than in a battery, but if you consider the short time that this energy is delivered in, the difference becomes even greater! Using the numbers above, the power output of an AA battery is about 2 watts. But the power of the lightning dwarfs the battery: 750 trillion watts (7.5 billion J / 2.0 x 10^-5 seconds) – mdh8b Jul 24 '13 at 2:07
• I was wondering about this but I picked yours because your explanation is very clear to me. – Sedumjoy Jan 11 '18 at 5:37

## protected by W5VO♦Jun 1 '17 at 19:21

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