Calculate how many electrons pass through the miner’s lamp during the tour of the mine shaft

Imagine being able to count electrons – those tiny, invisible particles no one has ever seen. They are so small that we can’t even picture them, let alone count them. But if we know the charge each one carries and the total electric charge that passes through a circuit, we can precisely calculate how many there are.

As already known, each miner carries a bulb hooked on the front of the helmet. The miner takes 3 hours to go through the window and return from the cave. It is also known that the current flowing through the lamp is 300 mA, and the battery accumulates the amount of charge of 1.5 Ah. The miner went on a long tour of the grove mine, but it is not certain how long the light bulb may be and whether it will be possible to visit the grove mine during that time.

a) It is important for a miner to know how much time the lamp will light up?

While a curious physicist might be interested in the following:

b) How much (for how long can the lamp be illuminated), the electrons go through the current circuit?

c) Calculate how many years each inhabitant of the Earth should count? If we assume that the electrons can be counted individually and that each inhabitant can count three electrons in one second, and that the Earth has 7 billion inhabitants.

Explanations:

a) The current I is: 

Which means the miner had time to go through the grove mine.

b) The number of electrons can be calculated from the expression:

where “e” is the charge of one electron that it is    or 

then N is: 

c) Each inhabitant must count the N’ electrons

If every inhabitant counts three electrons in one second, one inhabitant will count for one year.   

So every inhabitant would have to count:

Conclusion:

We can’t see electrons, and counting them would take over 50,000 years!

But thanks to physics and a few formulas, we can calculate them with precision —

and gain insight into the invisible world around us.

Aziza