Power

Power is an important concept in physics that helps us understand how quickly energy is used or work is done in everyday devices and machines.

Definition of Power

Power is the rate at which energy is transferred or converted from one form to another. It tells us how quickly work is done or energy is used.

Power is measured in watts (W). One watt is equal to one joule of energy transferred per second.

The formula for power is:

$$\text{Power} = \frac{\text{Energy transferred}}{\text{Time}}$$

where energy transferred is in joules (J) and time is in seconds (s).

For example, if a machine transfers 1000 J of energy in 10 seconds, its power output is:

$$\text{Power} = \frac{1000 \text{ J}}{10 \text{ s}} = 100 \text{ W}$$

Power in Electrical Circuits

In electrical circuits, power can be calculated using the voltage and current:

$$\text{Power} = \text{Voltage} \times \text{Current}$$

where voltage (V) is in volts and current (I) is in amperes (A), so power is in watts (W).

This formula shows how much electrical energy is transferred each second in a circuit.

Electrical devices have power ratings, which tell you how much power they use when operating normally. For example:

• A 100 W light bulb uses 100 joules of electrical energy every second.
• A 2 kW kettle uses 2000 joules of energy every second.

Knowing the power rating helps you understand energy consumption and costs.

For example, if a device has a voltage of 12 V and a current of 2 A, the power is:

$$P = V \times I = 12 \times 2 = 24 \text{ W}$$

Other useful formulas involving resistance (R) are:

$$P = I^2 \times R$$

and

$$P = \frac{V^2}{R}$$

where resistance is in ohms ($\Omega$). These formulas help calculate power when resistance is known.

Power in Mechanical Systems

In mechanical systems, power is the rate at which work is done. The formula is:

$$\text{Power} = \frac{\text{Work done}}{\text{Time}}$$

Work done is measured in joules (J) and time in seconds (s), so power is in watts (W).

Power can also be related to force and velocity. If a force $F$ moves an object at a velocity $v$, the power output is:

$$\text{Power} = \text{Force} \times \text{Velocity}$$

where force is in newtons (N) and velocity in metres per second (m/s).

This formula is useful for engines and machines where a force moves something at a steady speed.

For example, if an engine applies a force of 200 N to move a car at 10 m/s, the power output is:

$$P = F \times v = 200 \times 10 = 2000 \text{ W} = 2 \text{ kW}$$

Learning example: A cyclist pedals with a force of 150 N and travels at 5 m/s. Calculate the power output.

Using $P = F \times v$:

$$P = 150 \times 5 = 750 \text{ W}$$

So the cyclist is producing 750 watts of power.