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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

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    $\begingroup$ At high voltage, you are more likely to have dielectric breakdown. $\endgroup$ – wcc Apr 15 at 18:37
  • $\begingroup$ What happens if I take a gigantic battery, i.e. one that can supply up to one kiloamp of current, with a 1 V voltage and connect its terminals to your hands? Now what happens if I connect a smaller, battery i.e. one that can supply only up to 1 amp, with a voltage of 1 kV, across your hands? $\endgroup$ – DanielSank Apr 15 at 18:38
  • $\begingroup$ You may find this question relevant: physics.stackexchange.com/q/141331. $\endgroup$ – DanielSank Apr 15 at 18:39
  • $\begingroup$ The gigantic battery would transfer 100w to me through my hands while the smaller battery transfers 1000w thereby being more dangerous? $\endgroup$ – Ubaid Hassan Apr 15 at 18:44
  • $\begingroup$ that post you linked me created more questions for me than it answered. ;-; What is that OP talking about? A low resistance=stronger heating effect? I thought it would be the opposite. $\endgroup$ – Ubaid Hassan Apr 15 at 18:53
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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.

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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 $V_2\cdot A_2$, too).

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

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

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  • $\begingroup$ why not the reverse? why not have the current going into the resistor and then determining the voltage? $\endgroup$ – Ubaid Hassan Apr 15 at 20:22
  • $\begingroup$ Imagine yourself the voltage as a force, the resistor as a body (mass), and the current as a resulting motion (acceleration). It's not possible accelerate the body without the force, the force is necessary condition for the acceleration. Similarly, there is no current without a voltage, the voltage is the basis. Your battery has a voltage without a current - if you connect the poles with a conductor, you enable the current to flow. The voltage is a constant, the amount of the current accommodates to the impedance. $\endgroup$ – MarianD Apr 15 at 21:36
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    $\begingroup$ @UbaidHassan Another way to think about this is: The power plant makes it their job to ensure constant voltage, not constant current. They do this by adjusting how much power leaves the plant. If you try to draw more current, they burn more coal (or whatever). So why does voltage determine the current, and not vice versa? Because the power plant does its best to ensure voltage remains constant no matter how much current you draw. $\endgroup$ – Jahan Claes Apr 15 at 21:48
  • $\begingroup$ @UbaidHassan The power plant isn't sending you a fixed chunk of energy. It's TRYING to send you a fixed chunk of voltage; the energy just comes along for the ride. $\endgroup$ – Jahan Claes Apr 15 at 21:51
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    $\begingroup$ I just had an Aha! moment. thanks guys I finally understand that voltage is a constant whereas current varies with resistance :D $\endgroup$ – Ubaid Hassan Apr 15 at 23:33
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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.

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    $\begingroup$ The article you refer to on human impedance variability I believe deal with the internal body impedance paths through the heart and does not include the skin impedance which, when dry and not otherwise compromised, is the bodies main protection against electric shock from sources outside the body and varies from a couple of thousand to a hundred thousand or more ohms, depending on the magnitude, frequency, waveshape, etc. of the voltage source. $\endgroup$ – Bob D Apr 16 at 14:43
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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.

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  • $\begingroup$ I understand that a low voltage on a human means a lower current because 10000I=V, but that low voltage in this case comes with the trade off of a high current due to the step down transformer used for the house. this means that a low voltage would deliver large current to the human would it not? $\endgroup$ – Ubaid Hassan Apr 15 at 19:20
  • $\begingroup$ No. A human being is also a conductor, and as such, a human being also follows Ohm's law. $\endgroup$ – David White Apr 15 at 21:14
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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.

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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.

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