Charging Mobile Phones

Electricity and Magnetism Level 2

Max’s cell phone has exactly 10% battery life left. He knows it takes 2 hours to fully recharge it from there.

After the charge begins, when will his phone have exactly 55% of battery life left?

Details and Assumptions:

  • Neglect battery drainage and running apps during phone charging.
  • The voltage of the charger is constant throughout the time.
In less than 1 hour In exactly 1 hour In more than 1 hour

Michael Huang by Michael Huang , 29, USA

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2 solutions

I think you could think of the battery of the phone as a capacitor, your plug as a voltage source and the wire as a resistor (all wires have some resistance). Then, you would use the RC equation for voltage across the capacitor (which proportional to the charge), which is a reversed exponential which grows at a decreasing rate

8 Helpful 0 Interesting 0 Brilliant 2 Confused

RC Law should be useful as the faster shortcut, though the rate is not constant throughout. You can observe the relationship between the flowing current and the voltage difference between phone and charger here.

Michael Huang - 3 years, 3 months ago
Jon Tavasanis
Mar 9, 2018

He needs a 45% increment of battery charge level. As it is less than 50%, time would be less than 1 hour.

3 Helpful 0 Interesting 0 Brilliant 1 Confused

How do you know the charging takes less than an hour less than a half? You will need to state how the rate is not constant throughout the time.

Michael Huang - 3 years, 3 months ago

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The problem assumes that "The voltage of the charger is constant throughout the time". If a 100% charge takes 2 hours, then 55%-10% = 45% charge would take 45/90*120 minutes = 54 minutes.

Jon Tavasanis - 3 years, 3 months ago

It should take exactly one hour ...as it is originally 10% charged ND it takes further 2 hrs to charge it from there .( ND not from 0%) 🌟

90% 🔋 is charged in two hours or 120 minutes , so 9% 🔋 will be charged in 12minutes. 🌟

U need to charge to 55 % ...ND it is originally 10% charged . So difference will be of 45%. So acc. To mathematics ...45% 🔋 will be charged in 60 minutes.

( 9% in 12 min) (18% in 24 min) (27% in 36 min) (36% in 48 min) (45% in 60 min)

Aditya Anand - 3 years, 2 months ago

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Right. Exactly 1 hour. Sorry for my fault: "it takes 2 hours to fully charge it from there [10% of charge]".

Jon Tavasanis - 3 years, 2 months ago

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