Define power as work done per unit time and also as energy transferred per unit time; recall and use the equations (a) P = W / t (b) P = ΔE / t

1.7.4 Power 📈

Definition

Power is the rate at which work is done or energy is transferred. In other words, it tells us how fast energy is being used or moved. Think of it as the speed of a river: the faster the water flows, the more water passes a point each second.

Key Equations

Units & Symbols

• \$W\$ – Work or Energy (joules, J)
• \$\Delta E\$ – Change in Energy (joules, J)
• \$t\$ – Time (seconds, s)
• \$P\$ – Power (watts, W) – 1 W = 1 J s⁻¹

Practical Examples

1️⃣ A 60 W light bulb uses 60 joules of energy every second.

2️⃣ A car engine that does 10 000 J of work in 5 s has a power of

\$P = \frac{10\,000\;\text{J}}{5\;\text{s}} = 2\,000\;\text{W}.\$

3️⃣ A laptop that consumes 15 W runs for 4 h (14 400 s). The total energy used is

\$E = P \times t = 15\;\text{W} \times 14\,400\;\text{s} = 216\,000\;\text{J}.\$

Analogies to Help Remember

• ⚡ Power is like the speed of a car: the faster the car moves, the more distance it covers per second.
• 💧 Think of power as the flow rate of water in a pipe – higher flow means more water passes a point each second.
• 🎬 Power is the “rate of action” in a movie: a faster movie (higher frame rate) shows more frames per second.

Practice Problems

1. A 200 W heater runs for 3 h. How many joules of energy does it use?
2. A machine does 5 000 J of work in 20 s. Calculate its power.
3. If a device has a power of 50 W, how much work does it do in 10 s?

Quick Check

- Write the two main equations for power.

- Convert 3 W to joules per second.

- Explain why a higher power rating means a device can do more work faster.