What are the SI base units of the watt, the unit of power?
- power = energy ÷ time, so W = J s−1.
- energy = force × distance, and N = kg m s−2, so J = kg m s−2 × m = kg m2 s−2.
- W = kg m2 s−2 ÷ s = kg m2 s−3.
Answer: kg m2 s−3
SI units
AS Level Physics · Physical quantities and units. A short explanation of the idea, the rules to remember, the mistake to avoid, a worked example and practice questions with answers.
The idea
All units in physics are built from a small set of base units. At AS Level you need five: the kilogram, metre, second, ampere and kelvin. Every other unit is a derived unit, made by multiplying or dividing base units. To find the base units of a quantity, write a simple equation for it and replace each quantity by its units.
An equation is homogeneous when every term in it has the same base units. A correct equation is always homogeneous. Pure numbers such as 2, ½ and π have no units. A homogeneous equation can still be wrong, for example if a number is missing.
Prefixes are a short way to write powers of ten, such as 1 km = 103 m.
Rules to remember
- Base quantities and units: mass (kg), length (m), time (s), current (A), temperature (K)
- newton: N = kg m s−2 (from F = ma)
- joule: J = N m = kg m2 s−2; pascal: Pa = N m−2 = kg m−1 s−2
- coulomb: C = A s (from Q = It); volt: V = J C−1 = kg m2 s−3 A−1
- Small prefixes: pico p 10−12, nano n 10−9, micro μ 10−6, milli m 10−3, centi c 10−2, deci d 10−1
- Large prefixes: kilo k 103, mega M 106, giga G 109, tera T 1012
- Homogeneous equation: every term has the same base units
Common mistake
Giving N or J in an answer that asks for base units. The newton and the joule are derived units, so break them down fully into kg, m and s.
Worked example
Practice questions
Try each one, then open the answer.
1. What are the SI base units of the volt?
- Akg m s−3 A−1
- Bkg m2 s−2 A−1
- Ckg m2 s−3 A
- Dkg m2 s−3 A−1
Show answer
Answer: D. V = W/Q. Energy is kg m2 s−2 and charge is A s, so the volt is kg m2 s−2 ÷ (A s) = kg m2 s−3 A−1.
2. What are the SI base units of the pascal (the unit of pressure)?
- Akg m−1 s−2
- Bkg m s−2
- Ckg m2 s−2
- DN m−2
Show answer
Answer: A. Pressure = force ÷ area = (kg m s−2) ÷ m2 = kg m−1 s−2. N m−2 is correct but not in base units.
3. The wavelength of an X-ray is 0.15 nm. What is this wavelength in picometres?
- A1.5 pm
- B15 pm
- C150 pm
- D1.5 × 105 pm
Show answer
Answer: C. 0.15 nm = 0.15 × 10−9 m = 1.5 × 10−10 m, and 1 pm = 10−12 m, so this is 150 pm.
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