Units and dimensions – identifying the S.I. unit of power Evaluate the statement: “The unit of power in S.I. units is kilowatt.”

Introduction / Context:Power, the rate of doing work or transferring energy, has a well-defined S.I. unit. While multiples such as kilowatt are in widespread use, the base S.I. unit must be identified correctly in examinations to avoid conceptual errors.

Given Data / Assumptions:

• S.I. base and derived units are used.
• 1 watt = 1 joule per second.
• Multiples like kilowatt (kW) are allowed but are not the base unit.

Concept / Approach:The S.I. derived unit of power is the watt (W). Kilowatt is a decimal multiple (1 kW = 1000 W). Statements that equate the S.I. unit itself to kilowatt are therefore inaccurate; the correct phrasing is “the S.I. unit is the watt.”

Step-by-Step Solution:Recall definition: power P = dW/dt with unit J/s.1 W = 1 J/s = 1 N·m/s = 1 kg·m^2/s^3.Kilowatt is a multiple: 1 kW = 10^3 W.Hence the statement “unit is kilowatt” is false.

Verification / Alternative check:Electrical nameplate ratings often list kW or MW for convenience, but standards (ISO, IEC) define the S.I. unit of power as the watt.

Why Other Options Are Wrong:

• “True only for electrical systems” or “only for large machines”: the unit does not depend on application or magnitude.
• Option (e) contains the correct information but (a/b) asks truth value; the correct truth value is “False.”

Common Pitfalls:Assuming commonly used multiples are the fundamental units. Always distinguish base/derived units from their decimal multiples.

Final Answer:False