# Why does grounded imply V = 0 ?

## Main Question or Discussion Point

Why does "grounded" imply "V = 0"?

My *physical* understanding of the term "grounded" is this: A grounded conductor has access to an infinite supply of electrons.

Apparently, however, if a conductor (a sphere, a plate, etc.) is grounded, it's automatically at potential V = 0. Why is this? I thought the potential could be whatever we want it to be for any charge configuration, so I'm sure V = 0 is just a convenient choice for a grounded conductor. Still, I'm not sure why this is. Can someone help?

For the record, I know the potential inside a conductor is constant, so it makes sense that if V = 0 at one point in a conductor, it must be 0 everywhere else in the conductor.

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jtbell
Mentor

The "grounded" condition is easily reproducible in the laboratory. If you ground several objects, you can be sure they're at the same potential even without touching them together.

You're right. It is an arbitrary (and convenient practically) zero.
However, we tend to deal in potential differences, so that the absolute value of potential at some point is not always useful, whereas the difference in potential between it and some other point is.
Setting ground = zero just makes things easier.

cgw

Basically is it how the phases of the electrical system are connected. The voltage is a potential between phases. A wye connected 208 volt transformer has it's center leg connected to ground which we call 0. Then there is 120 volts between a phase pole and the ground pole and 208 volts between any two phase poles. An ungrounded delta transformer (lets say 240 volt) will have 240 volts between any two poles. I forget what you would get if you took a voltage between a pole and ground (maybe nothing). AC systems are grounded to provide a reference point so everything is at the right potential to everythig else (mostly for safety).

Astronuc
Staff Emeritus

You're right. It is an arbitrary (and convenient practically) zero.
However, we tend to deal in potential differences, so that the absolute value of potential at some point is not always useful, whereas the difference in potential between it and some other point is.
Setting ground = zero just makes things easier.
The key is that the zero potential is an arbitrary reference for the circuit.

In a conductor, the potential would be the same everywhere - in the case of electrostatics. If a potential difference is applied to a conductor, either by a battery (i.e. placing the ends of the conductor across the terminals of a batter) or applying a time varying magnetic field (inducution) to the conductor, the there will be a potential (voltage) difference in the conductor and current will flow (charges more or redistribute) in response to the voltage difference.

In the case of the three phase AC system cited, there is a line voltage measured with respect to ground, and a higher voltage (potential difference) measure from line to line (phase-to-phase). Normally there is a neutral line, which is grounded to a zero reference potential.

The ground (earth) was taken as an arbitrary zero reference potential long ago and has become a convention.

What I'm talking about specifically are "boundary value" problems in electrostatics. These problems frequently include some surface (a sphere, a cylindrical or spherical shell, a plate, etc.) that is "grounded." The automatic response is that the boundary conditions must be V = 0 on these conductors. Is this done just because it's nice to introduce some zeroes into differential equations because it makes solving them easier (or less ugly), and putting the zero of the potential somewhere else wouldn't be very helpful?

Here's another simple way to look at it. Imagine 2 unknown points in a circuit. Say you take a meter set to measure voltage and touch the probes to these two points and you read 5 volts. This does not mean one point is 5 volts and the other is 0 volts. One point could be 600 volts and the other 595 volts. Your meter just tells you the potential difference between the points.

Now that you know that, how can we ever compare actual voltages in my circuit to voltages in your circuit 800 miles away? We need a common point to test against. This is where earth ground comes in. Construction workers actually drive 6 to 8 foot copper rods into the earth, or more commonly connect to a water main, to provide a ground reference in a building. We now have a point which is designated as 0 volts, even though it may have a huge potential between the moon or an airship flying through dry air (The Hindenburg). But at least we can agree on a common point to designate other potential differences against.