Consider the following:

V = voltage
I = current
R = resistance
P = power = VI

M = mass
D = distance
T = time

C = speed of light = D/T
E = energy = MC^2 = M(D/T)^2

A = acceleration = D/T^2
F = force = MA = MD/T^2

We know that voltage is conveyed as a force. But what about the dimensions of I and R?

Well watts are defined in terms of power which equals energy divided by time or (M(D/T)^2)/T so P = MD^2/T^3. And since I = P/V we can work out the dimensions of current as being (MD^2/T^3) / (MD/T^2) = D/T and hencewise R = M/T.

So current is simply a velocity. That makes sense. But resistance...a measure of mass per time. What does that even mean?!

 

No that's not right.

E = M(D/T)^2 = MD^2T^2
P = MD^2T^2 / T = MD^2T
I = P/V = MD^2T / (MD/T^2) = D/T
R = M/T

Okay so same result...

 

We know that voltage is conveyed as a force.

We do? From the definition of force as F = ma, we see that it has dimensions MLT^-2, i.e., the product of mass and length over time-squared. In SI units, this is kg⋅m / s^2, which we call a newton.

Voltage is a measure of the energy per charge between two points, i.e., how much work would have be done to move a charge between the two points. So, voltage must have the dimensions of energy over charge. A convenient definition of energy is E = mc^2, which has dimensions M(LT^-1)^2 = ML^2T^-2. In SI units, this is kg⋅m^2 / s^2, which we call a joule. Charge is its own dimension -- we can measure it directly -- which we'll call Q, with SI unit C (coulomb).

So, the dimensions of voltage are joules per coulomb, J / C, which is obviously not the same thing as a newton.

Electric current is defined in terms of charge per unit time, i.e., C / s in SI units. As resistance is the ratio of voltage to current, we have R = V / I = (J /C) / (C / s) = (J ⋅ s) / C^2.

Therefore, [R] = [J] / Q^2 = ML^2T^-1Q^-2.

In other words, resistance has dimensions of mass times area per square-charge time. Or, if we use current instead of charge as the fundamental quantity (which I think we do now), we have [R] = ML^2T^-1(IT)^-2 = ML^2T^-3I^-2. That is, resistance has dimensions of mass times area per time-cubed and current-squared. Personally, I prefer to call it an ohm and be done with it.

 

We know that voltage is conveyed as a force. But what about the dimensions of I and R?

Do we? Voltage is not a force, it is a potentional difference. It is the energy needed to move a charge from one place to another in an electric field. You can define a force per unit charge to any point in an electric field, but a voltage cannot be defined at a point, only between two points.

Voltage in more basic units is Joules per Coulomb. Joules can be reduced to more basic units. I am not sure Coulombs can be.

Bob

 

Okay so energy per unit charge. Yeah "we" really were way off.

 

Consider the following:

V = voltage
I = current
R = resistance
P = power = VI

M = mass
D = distance
T = time

You are missing one of the four base units of the SI system -- electrical current.

The preferred abbreviations are
M = mass
L = length
T = time
I = current

C = speed of light = D/T
E = energy = MC^2 = M(D/T)^2

A = acceleration = D/T^2
F = force = MA = MD/T^2

We know that voltage is conveyed as a force. But what about the dimensions of I and R?

Well watts are defined in terms of power which equals energy divided by time or (M(D/T)^2)/T so P = MD^2/T^3. And since I = P/V we can work out the dimensions of current as being (MD^2/T^3) / (MD/T^2) = D/T and hencewise R = M/T.

So current is simply a velocity. That makes sense. But resistance...a measure of mass per time. What does that even mean?!

Does current being a velocity REALLY make sense? If the electrical current in my resistor is 10 meters per second, what will my ammeter read in amperes?

Voltage is NOT a force. The voltage difference between two points is defined at the work needed to move a unit of charge from between two points, so it has units of energy per charge (1 volt is defined as one joule per coulomb).

Current is a base unit. Charge is the total current flowing past a point (or through an area) over a unit of time. (1 coulomb is defined as 1 ampere-second)

dim(V) = (M)(L^2)(I-1)(T^-3)
dim(I) = I
dim(R) = (M)(L^2)(I^-2)(T^-3)

 

And just to confuse it all Voltage is and has often been defined as Electro-Motive Force. It is potential (not kinetic) energy J/C.

 

And just to confuse it all Voltage is and has often been defined as Electro-Motive Force. It is potential (not kinetic) energy J/C.

But "electromotive force" is just a name (one that was coined sometime around 1824 as being qualitatively descriptive -- I'm not sure by who, I don't think it was Faraday, but he correctly identified it's origins in electrochemical cells shortly thereafter), not a definition. It is NOT a force, however its gradient is a force field.

Voltage is a broader concept than EMF, which generally refers to the source, such as a battery or a generator, that converts energy from some non-electrical form to electric energy. Voltage refers to the difference in electrical potential energy between two points. So while you can talk about the EMF of a battery (I personally prefer not to -- I hate the term EMF precisely because it misleads so many people), you don't talk about the EMF of a resistor (though some people mistakenly do).