What is Power?

What is Power?

Power is the rate at which work is done or the rate at which energy is transferred or converted. In other words, power tells us how quickly a job is performed. When more work is done in a given time, the power is greater.

Power

The SI unit of power is the Watt (W), which is equal to one joule per second (1 W = 1 J s⁻¹). Power of engines and machines is often quoted in horsepower (hp); 1 hp ≈ 745.7 W (commonly rounded to 746 W).

Average and Instantaneous Power

Average power over a time interval Δt is defined as the total work done (or total energy transferred) ΔW divided by the time interval:

P_avg = ΔW / Δt

Instantaneous power is the power at a specific instant of time and is defined as the time derivative of work:

P = dW / dt

Power Formulae and Useful Relations

• P = W / t for average power when W is the work done in time t.
• If a constant force F acts on a body and the body moves with instantaneous velocity v, then instantaneous power delivered by the force is the dot product:

P = F · v

• This means P = F v cosθ where θ is the angle between the force vector and the velocity vector. Power is maximum when force and velocity are parallel (θ = 0) and is negative when the force opposes motion (θ = 180°).
• For rotational motion, the instantaneous power delivered by a torque τ when an object rotates with angular speed ω is

P = τ ω

• Units: Watt (W) = J s⁻¹. Common multiples: kilowatt (kW) = 10³ W, megawatt (MW) = 10⁶ W.
• Energy unit based on power: kilowatt-hour (kWh) is a unit of energy: 1 kWh = 1 kW × 1 h = 3.6 × 10⁶ J.

Interpretation and Examples

• A 60 W bulb converts electrical energy into light and heat at a rate of 60 joules per second while it is on.
• A motor rated 2 kW delivers energy at the rate of 2000 J every second when operating at rated conditions.

Solved Example

Q1. A 60-watt bulb is switched on 24 hours a day and there is another 60-watt bulb that is turned on for only 12 hours. Find the energy consumed by both the bulbs in one day. Solution:

60 W bulb A is ON for 24 hours.

Energy consumed by bulb A = Power × Time = 60 W × 24 h = 1440 Wh = 1.44 kWh.

60 W bulb B is ON for 12 hours.

Energy consumed by bulb B = Power × Time = 60 W × 12 h = 720 Wh = 0.72 kWh.

Total energy consumed in one day = 1.44 kWh + 0.72 kWh = 2.16 kWh.

Average power over the 24-hour period = Total energy / Total time = 2.16 kWh / 24 h = 0.09 kW = 90 W.

Total energy in joules = 2.16 kWh × 3.6 × 10⁶ J/kWh = 7.776 × 10⁶ J.

Practical Notes and Common Points

• Electricity bills charge for energy consumed (kWh), not power. A high-power device used for a short time can consume the same energy as a low-power device used for a long time.
• When solving problems, keep track of units: convert hours to seconds when using SI base units, or convert joules to kWh using 1 kWh = 3.6 × 10⁶ J when required.
• Remember the vector form P = F · v - only the component of force in the direction of motion does work and contributes to power.