Electrical – measuring earth to line voltage as zero? Is that what it supposed to be

Warning

• FYI - some early AC/DC radio sets had live to mains chassis when operated from mains.

Equipment chassis is usually grounded to wiring ground via earth lead on power plug where provided.

In any sane regulatory environment, appliances without an earth lead are required by law to be "double insulated" so that internal metal parts are not touch accessible during operation. (Note: Double insulation nowadays seldom involves two layers of insulation - it is more a state of mind in manufacture and testing that leads to touch safe equipment. Usually :-). )

While a chassis should be "touch safe", never assume it is, because:

• There are non-sane regulatory environments,

• or ones where the authorities enforce the rules so little that they may be ignored and

• It is excessively common for people to do silly and dangerous things with mains wiring, despite being aware that people are reported to have died due to such things.

Wikipedia - appliance classes

They say:

Class I

• These appliances must have their chassis connected to electrical earth (US: ground) by an earth conductor (coloured green/yellow in most countries, green in the U.S., Canada and Japan). A fault in the appliance which causes a live conductor to contact the casing will cause a current to flow in the earth conductor. This current should trip either an overcurrent device (fuse or circuit breaker (CB)) or a residual-current device (RCD) also named as residual current circuit breaker (RCCB), or (ground fault circuit interrupter (GFCI)) or also, residual current operated circuit-breaker with integral overcurrent protection (RCBO). which will cut off the supply of electricity to the appliance.

Class II - See also: double switching (and double insulated)

• A Class II or double insulated electrical appliance is one which has been designed in such a way that it does not require a safety connection to electrical earth (US: ground).

  The basic requirement is that no single failure can result in dangerous voltage becoming exposed so that it might cause an electric shock and that this is achieved without relying on an earthed metal casing. This is usually achieved at least in part by having two layers of insulating material surrounding live parts or by using reinforced insulation.

  In Europe, a double insulated appliance must be labelled Class II, double insulated, or bear the double insulation symbol (a square inside another square)..

Class III

• A Class III appliance is designed to be supplied from a separated/safety extra-low voltage (SELV) power source. The voltage from a SELV supply is low enough that under normal conditions a person can safely come into contact with it without risk of electrical shock.

  The extra safety features built into Class I and Class II appliances are therefore not required. For medical devices compliance with Class III is not considered sufficient protection.

You seem to have voltage and current conflated.

Voltage is more properly called electromotive force. It does not, in itself, flow, or transfer energy.

Current (usually measured in amperes) is a measure of how much electric charge is moving per unit of time. Current is also not, in itself, a flow of energy.

The flow of energy is called power. To have power, you need both current (\$I\$) and voltage (\$E\$). The power is equal to the product of the two:

$$ P = IE $$

It helps to think about this in terms of analogous mechanical systems, since we can observe mechanical systems directly with our senses. Mechanical systems also have power, where it is equal to the product of force and velocity:

$$ P = Fv $$

If you have force but no velocity, you have no power. An example would be a rubber band stretched between two stationary supports. The band is exerting a force on the supports. This tension is potential energy. But, nothing is moving, and none of that energy stored in the stretched band is being transfered to anything else.

However, if the band can move the supports, now we have velocity. As the band moves the supports, the energy stored in the stretched band will be converted to kinetic energy in the supports. The rate at which this energy transfer happens is power.

Voltage is a force that moves electric charge. Current is the velocity of electric charge. Resistance is how easy it is to move the supports.

Here's a mechanical system that's more analogous to your circuit:

We have a rigid ring, attached to a motor that applies some force to turn it. Also attached to the ring, we have a brake, which resists the turning of the ring. For this analogy to be proper, this has to be a brake that provides a force proportional to the velocity of the ring moving through it. Imagine it's coupled to a fan, so as the ring turns faster, the fan turns faster, creating more aerodynamic drag.

If the motor is applying a force of \$1kN\$, then the brake must be applying an equal force in the opposite direction. If the brake's force is not equal to the motor's, then the ring will experience a net force that will accelerate or decelerate it until the brake's force is equal, and the ring turns at a constant speed. Thus, if the force of the motor is constant, the speed of the ring is a function of the strength of the brake. This is analogous to Ohm's law.

What other forces are acting on the ring? Since we are considering an idealized system with no friction, there are none. If you were to insert strain gauges at points A and B, you would measure a difference between them. B is being compressed as the motor shoves the ring into the brake against its resistance, and A is being stretched as the motor sucks it out of the brake.

But what's the difference between B and C? there is none. If that's not intuitively obvious, consider that you must cut a gap in the ring and insert your hand so this machine can smash it. Is there a point at which you'd prefer to do this? No, your hand will be equally smashed regardless of where you do it on the left side of the ring.

The forces measured by the strain gauges are analogous to voltage. We can only measure voltages relative to some other voltage. That's why your voltmeter has two probes. Wherever you put the black lead is defined as "0V". So, the scenario you present in your question is like measuring the difference between B and C: it is zero.

This seems a little weird, because we know there is a compressive force on that entire side of the ring. It seems like that should be good for something. But consider this: the weight of all the gas in Earth's atmosphere results in a pressure at sea level of about 15 pounds per square inch. Does this mean we can make a machine that's powered just because it's exposed to this pressure? No. In order to do work with this atmospheric pressure, we need a difference in pressure. Without a difference, we can't make the air move. Consider again the definitions of power above, and it should become clear how this is true.