Question about Electrical Energy

[CrazyCrux]

I know that energy cannot be created nor destroyed. However, I also know that voltage is basically electrical potential energy. So, how can a transformer exist? In terms of classical mechanics, in order to increase the PE of say, a ball, you must lift it (expending energy) higher above the gravitational center of the earth. However, with transformers I don't see any immediate expenditure of energy that would allow such a drastic (200V to 15kV) increase in potential energy. Can someone explain this to me, please?

 

[anorlunda]

Good for you to never question conservation of energy. On this planet, energy is always conserved.

Transformers do conserve energy. But the rate of electric energy (which we call power) is V*I, voltage times current, not voltage. Your idea of electric potential as energy is a bit too simplified. Try starting here

https://en.wikipedia.org/wiki/Electric_potential
https://en.wikipedia.org/wiki/Electrical_energy

A key point, that I think you miss is that if we use a voltmeter to measure the voltage of a transformer, the voltmeter always has two wires. Voltage in an electric circuit is always the difference in potential between two points. The absolute electric potential, plays no role in circuit analysis.

 

[CrazyCrux]

Good for you to never question conservation of energy. On this planet, energy is always conserved.

Transformers do conserve energy. But the rate of electric energy (which we call power) is V*I, voltage times current, not voltage. Your idea of electric potential as energy is a bit too simplified. Try starting here

https://en.wikipedia.org/wiki/Electric_potential
https://en.wikipedia.org/wiki/Electrical_energy

A key point, that I think you miss is that if we use a voltmeter to measure the voltage of a transformer, the voltmeter always has two wires. Voltage in an electric circuit is always the difference in potential between two points. The absolute electric potential, plays no role in circuit analysis.

I think I understand now. Thank you for the explanation.

 

[Drakkith]

However, with transformers I don't see any immediate expenditure of energy that would allow such a drastic (200V to 15kV) increase in potential energy.

Voltage isn't a measure of potential energy, it's a measure of electric potential. Electric potential is a measure of the work required to move a unit of charge from its current position to infinity. Notice that I said "unit of charge". If I place a particle with a charge of three coulombs in an electric field, find its electric potential energy, and then divide out the charge, I no am longer talking about the particle, but about the field. When we give a voltage, we aren't saying that every single charge is given X amount of potential energy. Instead, voltage and electric potential are properties of the field. This allows us to greatly simplify and generalize our analysis of electrical circuits.

In a simple example like a single particle in free space, it's easy to say that voltage and the potential energy of a single particle are related. However, in an electrical circuit, things change drastically. We can't point to any individual charge and say that it will expend X amount of energy. Instead we are talking about the bulk behavior of huge numbers of charges. When the number of charges is something like $10^{20}$, the particulars of any single particle just don't matter. A charge may accelerate under the influence of the applied field for a short time and then lose all of its energy in a collision with an ion in the conductor. Or it may scatter and lose only some of its energy. Or it might be moving the opposite way as the current flow due to its thermal motion. All of these things can be simplified down thanks to the huge number of charges we're dealing with.