# 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!