Power and Energy

4.3. Power and Energy#

4.3.1. Power#

Power is the rate of doing work in an electrical system i.e. how quickly energy is being transferred or used. It is measured in Watts (W).

The formula is:

\[P = V \times I\]

  • P = Power in watts (W)

  • V = Voltage in volts (V)

  • I = Current in amps (A)

One watt means one joule of energy used every second.

Question 1

Imagine you power a small LED. It glows brightly, but you know LEDs use very little power. How much, exactly?

The specifications for the LED say:

  • Voltage across LED: 3 V

  • Current through LED: 0.02 A (20 mA)

Solution
\[P = V \times I = 3 \times 0.02 = 0.06 \;W\]
Question 2

You plug your phone into its charger. The charger label says “5V, 2A output.” How much power can it deliver?

Solution

Solution is locked

4.3.2. Energy#

Energy is the total amount of work done or stored. It is measured in Joules (J), which are watt-seconds. In other words a joule is one watt of power used for one second.

\[\text{Energy} = \text{Power} \times \text{Time}\]

Watt-Hours (Wh)#

A watt-hour is a more convenient unit than Joules for many situations. One watt-hour is of energy is 1 watt of power for 1 hour.

  • 1 W for 1 hour = 1 Wh

  • 10 W for 1 hour = 10 Wh

  • 1 W for 10 hours = 10 Wh

Batteries and milliamp-hours (mAh)#

Batteries are often rated in milliamp-hours (mAh), which can be converted into watt-hours:

\[Wh = \frac{\text{mAh}}{1000} \times V\]
Question 3

Suppose your robot is powered by three fresh AAA batteries. How much energy is stored in them?

  • Each AAA = 1200 mAh at 1.5 V

  • 3 cells in series = 4.5 V

Solution
\[Wh = \frac{1200}{1000} \times 4.5 = 5.4 \;\text{Wh}\]

The batteries store 5.4Wh of energy, which can be used to power the robot.

Question 4

If the robot’s two motors are running continuously, how long before the batteries run out?

  • Total motor power: 4.5 W (2 × 2.25 W)

  • Battery energy: 5.4 Wh

Solution

Solution is locked