Worked example: volt in base units
Physical Quantities & Units - OCR A-Level Physics
Setup
The voltThe SI unit of potential difference and EMF. $1 \text{ V} = 1 \text{ J C}^{-1}$. is the unit of potential differenceThe energy transferred per unit charge between two points. Measured in volts.. To express the volt in SI base units, we substitute two definitions step by step: $V = W/Q$ (energy per unit charge) and $W = Fd$ (work done by a force over a distance).
Worked Example [3 marks]
Using $V = W/Q$ and $W = Fd$, express the volt in SI base units.
Show Solution
1
Base units of charge
$Q = It$, so $[Q] = \text{A s}$.
[1]2
Base units of work
$W = Fd$, so $[W] = [F][d] = (\text{kg m s}^{-2})(\text{m}) = \text{kg m}^{2} \text{ s}^{-2}$.
[1]3
Combine
$[V] = [W]/[Q] = \dfrac{\text{kg m}^{2} \text{ s}^{-2}}{\text{A s}} = \text{kg m}^{2} \text{ s}^{-3} \text{ A}^{-1}$.
[1]Answer
$1 \text{ V} = 1 \text{ kg m}^{2} \text{ s}^{-3} \text{ A}^{-1}$.
Common Mistake
HIGH
Wrong: Writing $1 \text{ V} = 1 \text{ J C}^{-1}$ as the final answer. The joule and coulomb are themselves derived units.
Right: Keep substituting until only the six base symbols remain. $1 \text{ V} = 1 \text{ J C}^{-1} = 1 \text{ kg m}^{2} \text{ s}^{-3} \text{ A}^{-1}$. The mark scheme will not accept a partial answer for an "SI base units" question.
Right: Keep substituting until only the six base symbols remain. $1 \text{ V} = 1 \text{ J C}^{-1} = 1 \text{ kg m}^{2} \text{ s}^{-3} \text{ A}^{-1}$. The mark scheme will not accept a partial answer for an "SI base units" question.
Examiner Tips and Tricks
- Lay each substitution on a separate line. OCR mark schemes credit each intermediate step.
- Watch the index on the second: charge brings $\text{s}^{+1}$ that combines with $\text{s}^{-2}$ from force to give $\text{s}^{-3}$.
- The same chain $W \to Q$ works for the ohm: $R = V/I$ gives $1 \, \Omega = 1 \text{ kg m}^{2} \text{ s}^{-3} \text{ A}^{-2}$.