# Not all voltages are created equal

#### xox

Joined Sep 8, 2017
838
I've heard people make claims such as that one could run a house off of the potential difference between the earth (ie. ground) and a tower for example. That is obviously untrue but I was nonetheless unable to formulate a decent explanation for why so. The best I could come up with was an analogous circuit which demonstrates how some huge voltages can in fact be a lesser than others.

The circuit on the left supplies 10kV DC to an LED which requires a 470K resistor to limit the current to roughly 10.6 mV. The one in the middle merely "presents" a voltage of 10kV. (And yet if it were just a dangling wire we might confuse it with the leftmost one.)

The right hand side shows what would happen if an LED were connected to the middle circuit going straight to ground. The voltage drops to less than 2V. (Which by the way may not even be enough to light an *actual* LED due to forward voltage requirements!)

Is there a name for this general principle?

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#### crutschow

Joined Mar 14, 2008
34,058
It's called a resistive voltage divider.

And yes, the right hand LED will certainly light since it has nearly 10mA going through it.

#### xox

Joined Sep 8, 2017
838
It's called a resistive voltage divider.

And yes, the right hand LED will certainly light since it has nearly 10mA going through it.
But specifically WRT to the "dangling wire" aspect in particular. Suppose there was a bare wire extending from a "black box" and you wanted to know the voltage of that wire and so connected a voltmeter from that to ground and read 5kV.

That voltage however is not actually capable of powering a large load. Very little to no current would flow in such a case. Moreover a resistor would have likely been calculated before attaching an LED had we NOT known the actual voltage source to be a high resistance divider.

#### DickCappels

Joined Aug 21, 2008
10,124
This kind of thing is real and has been a problem with ranchers for decades...

What is Stray Voltage and How Does it Impact Dairy Cows?
On Behalf of Bird, Stevens & Borgen, P.C. | Apr 16, 2019 | Stray Voltage |

Stray voltage, also known as stray current or stray electricity, is a reality. Many courts have addressed stray voltage–the concept is not new.
The concept of stray voltage is as follows:
All electricity leaving an electrical substation must return to that substation in order to complete a circuit. Unless that circuit is completed, electricity will not flow. The current leaves the substation on a high voltage line which eventually connects to some electrical ‘appliance.’ After exiting the ‘appliance’ that current must return to the substation.
Continued: https://www.birdjacobsen.com/blog/2019/04/what-is-stray-voltage-and-how-does-it-impact-dairy-cows/

#### crutschow

Joined Mar 14, 2008
34,058
Moreover a resistor would have likely been calculated before attaching an LED had we NOT known the actual voltage source to be a high resistance divider.
I fail to see what you find unusual about the situation.

If you have a wire coming out of a black box, then it's a simple matter to determine its voltage and its resistance (the Thevenin equivalent).

xox

#### xox

Joined Sep 8, 2017
838
What I meant was the fact that a given measurement of voltage doesn't necessarily imply any specific current drawing capacity. Then again maybe the multimeter would actually read a lower value in such situations (~2V in this case)? Not sure...

#### xox

Joined Sep 8, 2017
838
I fail to see what you find unusual about the situation.

If you have a wire coming out of a black box, then it's a simple matter to determine its voltage and its resistance (the Thevenin equivalent).

I get it now. It's simple to insert a resistance into the measurement in order to determine the "true" voltage and thus the multimeter would never have read 5 kV in such a case but rather ~2V as the LED in adjacent circuit is being driven by. Correct?

#### MrChips

Joined Oct 2, 2009
30,503
No. You do not need current to define voltage.
Voltage is a measure of electrical potential. It is a force much as how gravity is a force.

When two oppositely charged objects are separated a force field is created.

There can be different potentials along each imaginary line of force.

Here are examples of equipotiential lines, i.e. points where the potential is the same:

You create an electric field when you charge two parallel plates (as in a parallel plate capacitor).

Voltage V = charge Q / capacitance C

Move the plates further apart and the capacitance C will decrease resulting in a higher voltage V. No new charge Q was added.
The potential V increased because work was required to pull the two plates apart.

#### MrChips

Joined Oct 2, 2009
30,503
The gold leaf electroscope is of historical interest.
This is the earliest known instrument for measuring electrical potential.

#### MisterBill2

Joined Jan 23, 2018
17,855
A voltage source has some internal resistance if it exists in the real world. In simulations it may not have any internal resistance. And all real world voltage measuring devices draw some current. So connecting a real world voltmeter to a real world voltage source will alter that voltage as measured a small amount. The measurement will be correct while it is being made, but the voltage when the meter is disconnected will be different.

That gold leaf electroscope is an interesting device. It only draws current while charging, and it is rather difficult to read with much resolution. So while it can prove there is a voltage it is not very useful for anything else.

xox

#### BobTPH

Joined Jun 5, 2013
8,677

xox

#### dcbingaman

Joined Jun 30, 2021
1,065
It may help to keep in mind that voltage is just Joules per Coulomb of charge. That is how much energy is released or used to allow one coulomb of charge to move from one point to another. The opposite is also true, that is how many joules of energy are needed to push one coulomb of charge 'uphill' that is to 'charge' the voltage source. In your first circuit, granted the LED will light up but drop practically no voltage in comparison to 5KV. That 470K resistor has to dissipate that energy which is enormous being P=V^2/R there is 5KV^2/470K or 53 Watts of wasted power while the LED uses a mere 2V at 10mA say 20mW making the efficiency of turning on that LED less than 1-0.02/53 or 99.96% wasted power. And the high impedance is obvious being that the voltage will drop dramatically with any 'small' resistance load. If you look for say a 50W 470Kohm resistor on digikey or any other source, it is hard to find for the simple reason it probably could not handle the equivalent energy dumping per coulomb of charge.
The human body resistance can be down to less than say 5-50Kohms depending on how damp the human body is when in contact with a voltage, the current at 5KV would be 100mA more than enough to electrocute someone. And the power being dumped into the human body at that would be at least 5VK^2/50K or 500 Watts of power! You will most likely catch on fire! Not a good thing.

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xox

#### xox

Joined Sep 8, 2017
838
Right as mentioned in post #5 I see. So it basically just boils down to understanding Thevenin's theorem. Well I guess I've got some reading to do then...

#### MrChips

Joined Oct 2, 2009
30,503
The modern day version of the gold leaf electroscope is the electronic electrometer.
For example, this Keysight B2987A Electrometer has input resistance of 10PΩ, that is 10 x 10^15Ω ( 1 followed by 16 zeros!).

#### xox

Joined Sep 8, 2017
838
The modern day version of the gold leaf electroscope is the electronic electrometer.
For example, this Keysight B2987A Electrometer has input resistance of 10PΩ, that is 10 x 10^15Ω ( one followed by 16 zeros!).

View attachment 249128
Oh wow! So they are designed to account for that.

#### cmartinez

Joined Jan 17, 2007
8,181
The modern day version of the gold leaf electroscope is the electronic electrometer.
For example, this Keysight B2987A Electrometer has input resistance of 10PΩ, that is 10 x 10^15Ω ( 1 followed by 16 zeros!).

View attachment 249128
When I first read your post, I thought that you were talking about pico-ohms.... and then I thought, gee... that's an extremely low value ... but then I realized your were talking about peta-ohms! ... wow!

#### Tesla23

Joined May 10, 2009
542
A voltage source has some internal resistance if it exists in the real world. In simulations it may not have any internal resistance. And all real world voltage measuring devices draw some current. So connecting a real world voltmeter to a real world voltage source will alter that voltage as measured a small amount. The measurement will be correct while it is being made, but the voltage when the meter is disconnected will be different.

#### dcbingaman

Joined Jun 30, 2021
1,065
The modern day version of the gold leaf electroscope is the electronic electrometer.
For example, this Keysight B2987A Electrometer has input resistance of 10PΩ, that is 10 x 10^15Ω ( 1 followed by 16 zeros!).

View attachment 249128
I looked up the price for it, around \$17,000 on Newark! Outside of my budget

#### MisterBill2

Joined Jan 23, 2018
17,855

View attachment 249133
OK, got me on that one, although that is measuring the voltage across some resistance, which I suppose could be incredibly large. But certainly this is not a common setup.

#### crutschow

Joined Mar 14, 2008
34,058
although that is measuring the voltage across some resistance
When the meter is null then there is (ideally) no voltage across or current through the meter and its resistance looks infinite.

xox