Electron borrowing

Ever wonder how many electrons we borrow from the electric companies for our energy bills (aka, paying for electricity)? Say you use like 9600 mWH per hour (a random number), someone here tell me how many electrons are flowing to produce that kind of power. From there you can possibly compare it to your electric bill and figure out how much money we pay per electron. Not too challenging, have a go at it.

For more accurate results, perhaps someone should post the results of one of their electric bills to see some real world results. Have fun.

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o_o!
Science is fun.

Voltage = Energy/unit of Charge
Icurrent = unit of Charge/Time
Power = Energy/Time = Voltage*Icurrent

An electron in a current under a potential difference (voltage) of 1 has −1.60217653*10^−19 Joules of kinetic energy, some of this energy is lost due to resistance, but if the energy is continually put into the circuit then the voltage remains the same. The charge of an electron doesn't change thus the charge is equal to the kinetic energy of an electron under a potential difference of 1.

V = (−1.60217653*10^−19)/(−1.60217653*10^−19) = 1

The kinetic energy of an electron under a potential difference of 1 is simplified by calling it an electron volt, Ev. Now that we have the facts we can answer your question. A watt is the SI unit for power, so megawatts need to be converted to watts by multiplying by 10^6.

P = 9600 mWH = 9.6*10^9 joules per hour

A second is the SI unit for time so we need to convert hours to seconds by multiplying hours by 3600 (60^2).

P = 9.6*10^9 joules per 3600 seconds = 2.67*10^6 joules per second, which is enough energy to accelerate a 1000 kg object from 0 to 263 kilometres per hour in a second, but we'll continue...

We will use algebra to figure out what we need to find the charge transferred per second or current.

I = C/T = P/V

I don't know what domestic voltage is used in your country, but in England it is 240, so I will use 240. You can easily finish the calculation by substituting 240 for your own voltage.

V = 240 volts
P = 2.67*10^6 joules per second
P/V = I = 2.67*10^6/240 = 11125 amps = 11125 coulombs per second.

Each electron has unit of charge of 1.60217653*10^−19 coulombs, thus 11125 amps = 11125/(1.60217653*10^−19) = 6.94*10^16 electrons.

Bearing in mind the huge amount of energy used we would be talking about the combined electrons moving backwards and forwards through a point in each of the circuits of thousands of homes after a large voltage has been broken down by a transformer.