To which of the following is the $W$ (watt) equal?

• A. $N\cdot m$
• B. $V\cdot A$
• C. $J/s$
• D. $\mathrm{kg}\cdot m^2/s^2$

Answer: (C)

Verified step by step guidance

1. Recall that the 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 mathematically as \(P = \frac{W}{t}\), where \(W\) is work or energy in joules (J) and \(t\) is time in seconds (s). Thus, the unit of power is joules per second (\(\frac{J}{s}\)).
3. Understand that 1 joule (J) is equivalent to 1 newton meter (N·m), since work done is force times displacement: \(W = F \times d\) with units \(N \cdot m\).
4. Recognize that electric power can also be expressed as voltage times current: \(P = V \times A\), where \(V\) is volts and \(A\) is amperes, which also results in watts.
5. Note that the unit \(kg \cdot m^{2} / s^{2}\) corresponds to a joule (J), so dividing by seconds (\(s\)) gives watts (\(W = \frac{J}{s} = \frac{kg \cdot m^{2}}{s^{3}}\)).