Why does voltage = energy/charge?

[babaliaris]

When you say $i = \frac{dq}{dt}$ it makes sense since current is the flow of charge over time. But why was voltage defined as
$v = \frac{dw}{dq}$ ? What made physicians define it in this way? Is there a mathematical way that can lead to this definition or
did they define voltage just on the spot?

 

[BvU]

Hi,

Yes: via force. Completely analogous to gravitational force and gravitational potential energy:

Electric field is force per charge.
Field is conservative so you can define a potential V with E as the spatial derivative of V.

Force times $dx$ is energy; force per charge times $dx$ is energy/charge.

 

[anorlunda]

It is a useful definition. Put a charge q at some point in a field where the potential is w. Now add a second charge of the same amount and sign. The charge is 2q, the potential is 2w, but the energy/charge remains unchanged. We call that ratio E (I don't like using v for that meaning.)

 

[sophiecentaur]

The Volt is based on Energy. A given charge (say 1 Coulomb) will require 1 Joule of Energy to move it between two plates with 1 Volt across them. It doesn't matter what the separation is; spread them wide and the Field is low and the Force is small but moved over a large distance ; bring them close together and the Force will be huge but the distance small. In both cases, the Force times Distance will still be 1J.
In another lab on another planet, the sizes of the units will be different so there's nothing particularly significant about the 1C,1J and 1V. It's just particularly convenient.

 

[alan123hk]

For those familiar with i=dq/dt and p=v*i, the definition v=dw/dq is natural and reasonable because p= v*i =(dw/dq)*(dq/dt) = dw/dt.

 

[PeroK]

When you say $i = \frac{dq}{dt}$ it makes sense since current is the flow of charge over time. But why was voltage defined as
$v = \frac{dw}{dq}$ ? What made physicians define it in this way? Is there a mathematical way that can lead to this definition or
did they define voltage just on the spot?

Well, $\frac{dw}{dq}$ is something. You could call it anything.

Whatever you call it, it has the same role to play in physics, which is determined by its definition alone; and not by what name you give it.

 

[Baluncore]

In order to reason, explain and discuss electrical things it is necessary to identify or construct a minimum set of what appear to be fundamental state variables and parameters, then give them agreed names and units. Our collection of terms has evolved over the ages to be internally consistent and functional.

From a component point of view, capacitance is defined as the ratio of charge to voltage;
C = Q / V; and the energy stored is; E = ½ · C · V²
Eliminate C, and you get; E = ½ · Q / · V ;
∴ E / Q = ½ · V