define power as work done per unit time
Energy Conservation: Power Defined
Power is the rate at which work is done or energy is transferred. In simple terms, it tells us how fast energy is being used or produced.
Power = Work Done per Unit Time
Mathematically, power is expressed as:
$P = \frac{W}{t}$
Where $W$ is the work done (in joules) and $t$ is the time taken (in seconds). The SI unit of power is the watt (W), where 1 W = 1 J s⁻¹.
Analogy: Water Flow
Think of power like the flow of water through a pipe. The amount of water (energy) that passes a point per second (time) is the power. A larger pipe or higher pressure (force) means more power.
Example: Light Bulb
A 60 W bulb uses 60 joules of energy every second. If you run it for 2 hours (7200 s), the total energy used is:
$E = P \times t = 60\,\text{W} \times 7200\,\text{s} = 432{,}000\,\text{J}$
Power in Everyday Life
- ⚡️ Electric motor: 200 W means it can do 200 J of work each second.
- 🚗 Car engine: 150 kW means it can deliver 150 000 J of work per second.
- 📚 Study: Your brain uses about 10 W of power while thinking.
Power Calculation Table
| Device | Power (W) | Time (s) | Work Done (J) |
|---|---|---|---|
| Flashlight | 5 | 120 | $5 \times 120 = 600$ |
| Laptop | 45 | 3600 | $45 \times 3600 = 162{,}000$ |
Exam Tip Box
Tip: When you see a question asking for power, remember the formula $P = \frac{W}{t}$. If the problem gives force and distance, first calculate work $W = F \cdot d$, then divide by time.
Also, check units carefully: power should be in watts (J s⁻¹). If you get joules or seconds alone, you need to divide or multiply accordingly.
Quick Practice Question
A 100 W light bulb is switched on for 3 hours. How much energy does it consume?
Solution: $E = P \times t = 100\,\text{W} \times (3 \times 3600\,\text{s}) = 1{,}080{,}000\,\text{J}$.
Revision
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