In SI measurement, which option correctly identifies the unit of power and its equivalent expression?

Introduction / Context:
Power quantifies the rate at which work is done or energy is transferred. In the International System of Units (SI), naming and dimensional equivalences are crucial for converting between energy, time, and power in engineering problems such as motor sizing, heat transfer, and electrical systems.

Given Data / Assumptions:

• Energy unit (SI): joule (J).
• Time unit (SI): second (s).
• Power is energy per unit time.

Concept / Approach:
By definition, power P = energy/time. Therefore, the SI derived unit of power is joule per second (J/s). This derived unit has the special name watt (W). The symbol W is ubiquitous across mechanical, thermal, and electrical contexts (e.g., P = V * I in circuits also yields watts). Joule alone is energy, not power, and lacks the per-second rate needed to characterize “how fast” energy is delivered.

Step-by-Step Solution:
Write definition: P = ΔE / Δt.Substitute units: joule/second.Recognize special name: joule/second = watt.Identify the option that includes both equivalent forms.

Verification / Alternative check:
Mechanical: 1 W = 1 N·m/s; Electrical: 1 W = 1 V·A; all reduce dimensionally to J/s, confirming the equivalence with watt.

Why Other Options Are Wrong:
Joule (a) is energy, not a rate.Watt (b) is correct but (d) is “more complete,” explicitly showing the equivalence J/s.Joule per second (c) is correct but again, (d) acknowledges both names.

Common Pitfalls:
Confusing energy (J) with power (W); mixing watt-hour (energy) with watt (power); dropping the time unit in rate calculations.

Final Answer:
Both (b) & (c)