Physics trivia

# Annual energy consumption of a smartphone

It takes a few hundred sextillion electrons to produce the charge in a cell phone battery. Will recharging it increase your energy bill?

First, let’s consider a cell phone whose battery has an electrical charge capacity of 1500 mAh. This unit, the milliamps-hour , can be converted into Coulombs by a very simple relationship: 1 mAh is equal to 3.6 C , so this battery holds up to 5400 C of electrical charge or about 3.3.10 22 electrons : 330 sextillion electrons, a very large number indeed.

The energy stored in the battery is the electrical potential energy , which can be calculated from the following equation:

In the above equation, q is the magnitude of the charge stored in the battery, in Coulombs (C), and ΔV is its operating electrical potential , about 4.2 V, so:

Therefore, a battery with a capacity of 1500 mAh stores an average of 22680 J (Joules) of energy. However, our electricity consumption is not measured in Joules , but in kWh (kilowatt hours), so we do the following conversion:

In this way, the 22680 J of energy is equivalent to about 0.006 kWh , that is, the amount of energy needed to fully charge the battery of a medium-sized cell phone. Considering that throughout the year a single full charge is carried out per day, we would have a consumption of 2.3 kWh. Taking the average price of a kilowatt-hour as BRL 0.45 , the cost would be around BRL 1.00 to recharge the cell phone battery each year. For comparison purposes, a shower turned on in the “winter” position consumes a power of 5.4 kWh , that is, in one hour of use, this appliance consumes 5.4 kWh ., more energy than your cell phone battery for a year.

Curiosity : A human being needs the intake of 2000 kcal daily to provide his body with the energy it needs for all its vital processes. This equates to 8,368,000 J , so everything you eat in a single day could recharge your cell phone for up to 368 days, just over a year!