Power

Welcome to the World of Power!

In your previous studies, you’ve looked at Energy (the ability to do work) and Work Done (the energy transferred by a force). But in Physics, we don't just care about how much energy is transferred; we often care about how fast it happens. That is exactly what Power is! Whether it's a supercar engine or a tiny LED bulb, understanding power helps us understand how efficiently and quickly our world works. Don't worry if it feels like a lot of formulas at first—we will break them down step-by-step.

1. Defining Power: The "Speed" of Energy

In simple terms, Power is the rate at which work is done or the rate at which energy is transferred.

The Formula

To calculate power, we use the following equation:

\( P = \frac{W}{t} \)

Where:
\( P \) = Power (measured in Watts, W)
\( W \) = Work done (measured in Joules, J)
\( t \) = Time taken (measured in seconds, s)

What is a Watt?

The unit of power is the Watt (W). One Watt is equal to one Joule of energy transferred per second (\( 1\text{ W} = 1\text{ J s}^{-1} \)).

Quick Review:
• Power is Work / Time.
• 1 Watt = 1 Joule per second.
• Faster energy transfer = Higher power.

2. Power and Moving Objects (\( P = Fv \))

Sometimes we need to calculate the power of a vehicle or a person moving at a constant speed. The syllabus requires you to be able to derive this equation from first principles. Don't worry—it's just a few simple steps!

Step-by-Step Derivation

1. Start with the basic power definition: \( P = \frac{W}{t} \)
2. Remember that Work Done is Force times distance: \( W = Fx \)
3. Substitute this into the power equation: \( P = \frac{Fx}{t} \)
4. Since velocity (\( v \)) is distance divided by time (\( \frac{x}{t} \)), we can replace that part of the formula.
5. We get: \( P = Fv \)

Important Note

This formula, \( P = Fv \), is used when a force \( F \) is moving an object at a constant velocity \( v \). This is common in exam questions involving cars driving against air resistance at a "top speed."

Did you know?
The "Horsepower" rating you see in car adverts is just another unit of Power! 1 Horsepower is roughly 746 Watts.

3. Electrical Power

In the "Resistance" part of this module, we look at how power applies to circuits. There are three main ways to write the electrical power equation. You can switch between them using Ohm's Law (\( V = IR \)).

The Three Equations

1. The Standard: \( P = VI \)
2. The "Heating" Equation: \( P = I^2R \)
(Useful when you know the current and the resistance of a wire)
3. The "Voltage" Equation: \( P = \frac{V^2}{R} \)
(Useful when you know the voltage across a component)

Energy Transfer in Circuits

If you want to find the total energy transferred (\( W \)) by a component over time, you multiply the power by the time:
\( W = VIt \)

Common Mistake to Avoid: Always make sure your time is in seconds! If a question says a bulb is on for 2 minutes, you must use \( 120 \) seconds in your calculation.

4. Efficiency: Getting the Most Out of Energy

In the real world, no machine is 100% efficient. Some energy is always "wasted," usually as heat due to friction or electrical resistance.

The Efficiency Formula

Efficiency is a ratio of what you want to get out versus what you put in.

\( \text{efficiency} = \frac{\text{useful output energy}}{\text{total input energy}} \times 100\% \)

You can also calculate efficiency using Power:
\( \text{efficiency} = \frac{\text{useful output power}}{\text{total input power}} \times 100\% \)

Key Takeaway: Efficiency is always a number between 0 and 1 (or 0% and 100%). If your calculation gives you 120%, stop and check your numbers—you’ve accidentally created energy, which violates the laws of physics!

5. The Kilowatt-hour (kWh)

The Joule is a very small unit of energy. If you looked at your home electricity bill in Joules, the numbers would be trillions! Instead, electricity companies use the kilowatt-hour (kWh).

What is it?

A kilowatt-hour is the amount of energy transferred by a 1 kW (1000 W) device running for 1 hour (3600 seconds).

Conversion to Joules

To convert kWh to Joules, use \( W = Pt \):
\( 1\text{ kWh} = 1000\text{ W} \times 3600\text{ s} = 3,600,000\text{ J} \) (or \( 3.6\text{ MJ} \)).

Memory Aid:
Think of kWh as a Big Bag of Energy. It’s not power, it’s energy.
• kW = Power (How fast)
• kWh = Energy (How much total)

Quick Summary Box

Equations to Memorize:
• \( P = \frac{W}{t} \)
• \( P = Fv \)
• \( P = VI = I^2R = \frac{V^2}{R} \)
• \( \text{Efficiency} = \frac{\text{Useful}}{\text{Total}} \)

Units:
• Power: Watts (W)
• Energy: Joules (J) or kilowatt-hours (kWh)