Which of the following correctly defines one watt in terms of base $\mathrm{SI}$ units?

• A. $\frac{J}{s}$ (joule per second)
• B. $\frac{V}{A}$ (volt per ampere)
• C. $\frac{C}{s}$ (coulomb per second)
• D. $\frac{N}{m}$ (newton per meter)

Answer: (A)

Verified step by step guidance

1. Recall that one watt (W) is the SI unit of power, which is defined as the rate of doing work or the rate of energy transfer over time.
2. Express power in terms of energy and time: power \(P\) is given by \(P = \frac{E}{t}\), where \(E\) is energy in joules (J) and \(t\) is time in seconds (s). Thus, one watt equals one joule per second, \$1\ \mathrm{W} = \frac{1\ \mathrm{J}}{1\ \mathrm{s}}$.
3. Next, express the joule (J) in base SI units: a joule is a unit of energy defined as \$1\ \mathrm{J} = 1\ \mathrm{N} \cdot 1\ \mathrm{m}$, where newton (N) is force and meter (m) is distance.
4. Recall that a newton (N) is defined as \$1\ \mathrm{N} = 1\ \mathrm{kg} \cdot \mathrm{m/s^2}\(, so substituting back, \)1\ \mathrm{J} = 1\ \mathrm{kg} \cdot \mathrm{m/s^2} \cdot \mathrm{m} = 1\ \mathrm{kg} \cdot \mathrm{m^2/s^2}$.
5. Therefore, one watt in base SI units is \$1\ \mathrm{W} = \frac{1\ \mathrm{J}}{1\ \mathrm{s}} = \frac{1\ \mathrm{kg} \cdot \mathrm{m^2/s^2}}{1\ \mathrm{s}} = 1\ \mathrm{kg} \cdot \mathrm{m^2/s^3}$.