Question

How does a step-up transformer, like the one used in a a battery-powered standby electrical system, not violate the Law of Conservation of energy when it changes 12V from a DC source to 110V of AC supply?

As a volt is essentialy the amount of energy (joules) used up by an electric charge, (coulombs) how does it make sense for a system to consume more energy than its input? Obviously, we have step-up transformers that work fine so we don't violate the Law of Conservation of Energy but I just dont get how this happens....

Answer 1

There is no violation since the power is constant
and conserved

`U_p*I_p=U_s*I_s`

If the voltage is higher, the current is smaller.

This principle is used for the transportation of electicity.

The voltage is very high but the current is very small.

`V_p/V_s=n_p/n_s`

Also, you have loss of energy in transformers, especially heating (Joule's losses)

PS :

You cannot connect directly your `24V` DC directly to a transformer, you must first convert your DC to AC with a converter. Then you can connect to your transformer `(24V)` to `(110V)`