Ttykuu

High $V$ low $A$ electricity is transformed into low $V$ high $A$ through a step down transformer for safer use in homes.

But how is it any safer? The wattage is the same for the pre-transformer charge flow, and the post-transformer charge flow. The energy both charge flows transfer is also the same.

Edit: by safety I’m referring to human contact

As @David White has pointed out, at low voltages the body's skin impedance when dry is very high. Therefore no matter how much current is available from the voltage source, only a small amount of current will flow through the body due to its high skin impedance per Ohm's law. So a 12 volt lead acid battery which has plenty of amps available will not cause an electric shock. (It could certainly cause burns if it contacts metal in contact with the skin).

The National Electrical Code (NEC) generally considers 60 Hz ac rms voltages that are less than 30 vrms at the output of an isolating transformer to be low risk with respect to electric shock under dry contact conditions. For this reason circuits connected to the secondary of a step down isolating transformer with output voltage less than 30 vrms is generally considered low risk of electric shock. These transformers, if they also comply with output current/power limits for fire considerations, are sometimes referred to as NEC Class 2 transformers.

When the voltage gets higher, or the skin gets wet, the skin impedance falls. Now the limiting factor is how much current is available from the voltage source. That will depend on the source impedance. For ac 60 Hz rms current the threshold of startle reaction is generally considered to be in the range of 0.5-5.0 mA. GFCI's are designed to trip at nominal 5 mA. From 5-10 mA the inability to let go becomes a possibility, depending on whether a child or adult. As the current through the body goes beyond 10-20 mA the the risk of ventricular fibrillation, and at very high currents, cardiac arrest, becomes greater.

There are many other factors involved in the risk of electric shock, too many to go into here. For example, at higher frequencies the skin impedance also drops (due to its capacitance). On the other hand, at higher frequencies a higher current is needed to produce the same physiological effect.

Various safety standards, in the US and International, publish voltage and current limits to reduce the risk of electric shock. They should be consulted.

ADDENDUM:

With regard to your following statement:

high V low A electricity is transformed into low V high A through a step down transformer for safer use in homes

If you are talking about the high voltage outside the home being stepped down to 120/240 vac by the utility transformer on the pole or under ground, the output voltages from those transformers do pose a risk of electric shock.

If, on the other hand, you are talking about step down transformers that step 120 vac down to 30 vac or less, such as transformers used in electronic equipment, or bell ringing transformers used within walls to power door bells, as I described above, then these transformers do reduce the risk of electric shock because the body impedance is very high at low voltage.

With regard to you comment to @David White, it doesn’t matter how much current is available from the step down transformer if the body impedance won’t allow it to flow. It is the current that actually flows in the body that determines the risk of electric shock.

Hope this helps.

Ohm's law is given by the equation $V=IR$. This equation can be solved for the current that exists in a conductor that has a given voltage difference across it, as $I=V/R$.

A human being with dry skin has a very high electrical resistivity, on the order of 100,000 ohms to a few million ohms. This is a good thing, because such a high resistance ensures a very small current flow when a human being becomes grounded against household voltage. However, there are various estimates of the minimum fatal dose of current through a human heart, but a common estimate is that 10 milliamps through a human heart will interfere with the electrical conductivity of the heart enough to produce a fatal arrhythmia. Thus, household current through a person will be small, but the minimal lethal current through that person is also small, so it is safest to run a household on a very low voltage to minimize the risk of a fatal electrical current going through any people in that house.

You are confused with the same wattage, supposing that wattage is determined by pre-transformed $V_1$ and $A_1$.

But the order of things is other:

• 
  $V_1$ is changed to $V_2$,


• then some resistor (a human body) is connected to the secondary, low voltage ($V_2)$ circuit,


• and the impedance of that resistor determines (by Ohm law) the $A_2$ (and - consequently - the wattage $V_2cdot A_2$, too).

Only after determining $A_2$ is determined $A_1$, too, to fullfil the equation $A_2/A_1 = V_1/V_2.$

Symbolically:

$$V_1 implies V_2\
V_2/ R implies A_2\
A_2 implies A_1$$

Most power sources have a fixed voltage (batteries, phone chargers, wall sockets) and can provide up to a certain limit amperes of current.

Phone chargers: always provide 5V, some are able to provide up to 2A while others can provide only 1A. The phone is responsible to "negotiate" with the charger how much current it draws so it doesn't damage the charger.

Wall sockets: always provide 230V AC (in Germany), but how much current is drawn depends on the connected device. Very little will be drawn by a phone charger, far more by a vacuum cleaner or an electric heater. Circuit breakers are in place that limit the current to 16A (usually) to prevent overheating wires.

So remember:

• Voltage is a property of a electrical source.


• Current will depend on the connected device(s)

Usually, if a device is connected to a variable voltage source, a higher voltage leads to a higher current. That is why high voltages are dangerous.

When you get a shock, the current is tiny. Only a few mA. You don't put much of a load on your household system. It is not like the lights in the house dim or anything. So the current capacity of the wires in the house is not really the issue.

But the higher the voltage, the more current flows through your body. If you get a 10mA shock from 120V, then you would get a 20mA shock from 240V. The sensation of being shocked, and the risk of permanent harm, are both related to the amount of current flowing. Greater current is more unpleasant, and ultimately greater risk of harm or death.

When electrical engineers work on circuits that transfer energy, the characteristic they use is called "impedance". To get power moved most efficiently, they "match" the impedances. There's a wikipedia article: https://en.wikipedia.org/wiki/Impedance_matching

Now impedance is simply the R in V=IR so we can compute the impedances for high and low voltage power and compare them with the impedance of a human.

Keeping the power at 2.4KW, let's compare 120 and 240V:

120V 20A => 6 ohms
240V 10A => 24 ohms

Note that the impedance was much higher with the higher voltage.

And what is the impedance of a human? The first hit on DuckDuckGo for me is a Fluke article:

"Human impedance variability has been shown to vary from 25 ohms to 180 ohms"
https://support.fluke.com/biomedical/download/asset/ppp085_impedance_educational.pdf

So we see that when shocking humans, our impedances will match better (and the shock will include more power) if we have the higher voltage.