How to calculate the power cost of charging a phone

 By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

27 March 2011

Victor Wahome is based in the remote town of Wanguru and he has noticed that, in the rural areas, people take their cell phones to kiosks for charging The cost is Sh15. He therefore wonders: “Based on the current unit cost of power, is it a fair price? Is it too expensive, or do the kiosk owners make a loss”

The first step in answering that question is to understand how electricity is sold. The unit of measurement is the kilowatt-hour. This is the amount of energy consumed by a 1,000-watt appliance running for one hour.

Now my electricity bill for February 2011 was Sh1,960 and I had consumed 150 units. This works out to about Sh13 per unit – all taxes, levies and adjustments included.

The next step is to find out the amount of electricity is consumed when charging a phone. One might be tempted to work this out using the storage capacity of a phone battery but that would be incorrect. The reason is that the charger warms up during the charging process – a clear indication that some of the energy is lost as heat.

So we use a different approach: find out how long it takes to charge the battery and then work out the electricity consumed by the charger during that time.

A battery’s storage capacity is stated in amp-hours (Ah); that is, how many hours can it sustain a current of one amp. Cell phone batteries have about 2Ah (usually written as 2,000mAh – milli-amp-hours).

We can use this information to find out long it takes to fully charge a completely empty battery; but we need to know the output current from a charger as well. I have one that reads 500mA; that is 0.5amp.

The charging time is therefore 2 divided by 0.5; that is 4 hours. That might sound too long, but it is because most of the time we don’t wait the battery to die completely before re-charging.

The last step is to work out the power consumption of the charger. Most of them draw about 0.1amp from the mains socket. At 240V, the power is 24W. Therefore it will consume about 96watt-hours in the 4 hours of charging.

We may round this off to 100Wh, or 0.1kWh to simplify the calculations. Now we are ready to find out the electricity cost of charging a phone. It is 0.1kWh multiplied by Sh13 per kWh; equals Sh1.30.

Therefore, the kiosk owners are not making a loss. However, one might wonder whether the Sh15 price isn’t too much. Well, just as in the case of matatus discussed here last week, power is not the largest cost in running the phone charging business; there are many other considerations.

At the end of the day, the price of an item depends more on what customers are willing to pay than what it costs to acquire. This is why businesses some times sell goods at a loss – because nobody is willing to pay a higher price.