# EWEEK PROBLEM OF THE DAY: FRIDAY

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Electrical engineers work on all kinds of projects in many different fields. Some work on large-scale projects, like urban power grids or communication systems, while others work on tiny microchips that are central to computers and cars. Electrical engineers work on some of our favorite entertainment, like video games and rollercoasters, as well as on some of the most important, life-saving technology, like medical tests, brain implants and prosthetics. One of the common ways we see their work is in our smartphones. Electrical engineers are behind the electronics used in Face ID authentication systems, Wi-Fi connectivity and batteries, among many other things.

You may have noticed that your microwave at home is an 800-watt microwave. This refers to the appliance load, or the amount of power the appliance uses when in use, and it is often measured in watts (W). Battery capacity, which can be measured in amp hours (Ah), refers to the amount of electric current, or energy, a battery can store and use to supply power to a device for a period of time. The maximum run time, in hours, of a battery can be calculated using the formula

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5.1 A team of electrical engineers wants a new smart phone’s battery to last for 12 hours. If the smart phone has an average appliance load of 2.6 watts, what does the battery capacity need to be, in amp hours? Express your answer as a decimal to the nearest hundredth.

5.2 The charging time t, in hours, of a phone with battery capacity c, in amp hours, can be calculated using the equation t = 2c. If Jared’s new phone has a battery capacity of 3.72 Ah, how many hours will it take his phone to fully charge? Express your answer as a decimal to the nearest tenth.

5.3 Marnie buys a smart phone from a different company. She heard that this phone takes only 4 hours to charge. Assuming Marnie’s smart phone has an average appliance load of 2.6 watts, how many hours can Marnie expect to use her phone before the battery dies? Express your answer as a decimal to the nearest tenth.