What Are the Dimensions and SI Units of Voltage?

[fran1942]

Hello, we have been asked:

i) State the dimensions of voltage. The work W done to move an amount of charge Q (coulombs) through a potential difference of V volts is given by W = VQ.
ii) state it's SI units.

Would I be correct to say
i) the dimensions are V=J/C or could I word it V=W/Q ?
ii) the SI units are joules and coulombs ?

Thanks kindly for any help.

 

[SammyS]

i) What are the fundamental "dimensions"? (They're NOT the same thing as units.)

ii) What combination of joules & coulombs? --- J·C, C/J, J/C, C^J or whatever other combination you can come up with?

 

[fran1942]

Thanks for your help. I have revised my answers based on your advice:

Would I now be correct to say:

i) the dimensions of Volts are: mass, distance, time and current
ii) the units are J/C

 

[SammyS]

ii) is correct.

i) Fundamental Dimensions are: mass, length, time, electric charge, and temperature, represented by the symbols M, L, T, Q, and Θ .

For example: dimensions of acceleration are: LT^‒2.

So, in addition to giving the dimensions of Voltage as: mass, distance, time and electric charge, you need to have an exponent where it's needed.

 

[CompuChip]

In addition to what Sammy said, maybe it is good to note the difference between physical quantities and their units.

i) the dimensions are V=J/C or could I word it V=W/Q ?

Both are correct in this case, but that is more or less coincidental. The point here is that the quantity V (voltage) is measured in units of volt, which is also denoted by V.

It is common to write the units of any quantity Q as [Q].
So if the formula for V is V = W / Q, then you could also write [V] = [W] / [Q] - i.e.: the units of V(oltage) are the units of W(ork) divided by the units of Q (charge).
If you use SI units, then [V] = V, [W] = J and [Q] = C.

 

[Mr.A.Gibson]

i) Fundamental Dimensions are: mass, length, time, electric charge,

Current is a fundamental unit, charge is definite in terms of current and time

 

[SammyS]

Yes, current is a fundamental unit, but we're looking at dimensional analysis. There's not universal agreement on whether charge or current should be fundamental. In what I looked up, the majority went with electric charge.

 

[ehild]

The problem is not well defined. Volt is also a SI unit, but not a basic one, just like joule and coulomb. Perhaps the unit of voltage in terms of base units (kg, m, s, A) is the question.

ehild

 

[ardheePrime]

In addition to what Sammy said, maybe it is good to note the difference between physical quantities and their units.
Both are correct in this case, but that is more or less coincidental. The point here is that the quantity V (voltage) is measured in units of volt, which is also denoted by V.

It is common to write the units of any quantity Q as [Q].
So if the formula for V is V = W / Q, then you could also write [V] = [W] / [Q] - i.e.: the units of V(oltage) are the units of W(ork) divided by the units of Q (charge).
If you use SI units, then [V] = V, [W] = J and [Q] = C.

the formula for V is V = W / Q
then W = F x L,
then Q = I x T
then Dimension for Force (F) is [M][L][T]^-2
dimension for Length (L) is [L]
dimension for current Electric (I) is [ I ]
dimension for Time (T) is [T]
so
V = W / Q = (F x L) / (I x T)
V = ([M][L][T]^-2[L]) / ([ I ][T])
= [M][L]²[T]^-2[ I ]^-1[T]^-1
= [M][L]²[T]^-3[ I ]^-1
dimension for Voltage is [M][L]²[T]^-3[ I ]^-1

 

[ardheePrime]

ii) is correct.

i) Fundamental Dimensions are: mass, length, time, electric charge, and temperature, represented by the symbols M, L, T, Q, and Θ .

For example: dimensions of acceleration are: LT^‒2.

So, in addition to giving the dimensions of Voltage as: mass, distance, time and electric charge, you need to have an exponent where it's needed.

I think electric charge not basic quantity...but Electric Current is basic quantity with dimension of electric current is [ I ]

 

[ardheePrime]

Hello, we have been asked:

i) State the dimensions of voltage. The work W done to move an amount of charge Q (coulombs) through a potential difference of V volts is given by W = VQ.
ii) state it's SI units.

Would I be correct to say
i) the dimensions are V=J/C or could I word it V=W/Q ?
ii) the SI units are joules and coulombs ?

Thanks kindly for any help.

i) dimension for Voltage is [M][L]²[T]^-3[ I ]^-1
ii) Joule and coulombs not SI units..because SI units using basic units of mks system
there are 7 basic quantity using SI units
Mass, Length , Time , Electric current, Temperature, Luminous Intensity, The amount of subtance. they are represented by the symbols for dimension [M], [L], [T], [ I ], [Θ], [J], and [N] .