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I'm trying to understand the difference between a power output in watts and a power capacity in watts, and I'm open to the possibility that I'm thinking about it all wrong.

If I want to charge a battery with a 2 watt-hour capacity, how long is it going to take me if I'm using a power source with a continuous output of 2 watts?

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Do you mean 2Wh for capacity? Which is 2W × 1hr. –  jippie Mar 7 at 18:41
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... or 1W × 2hr, or 0.5W × 4hr, etc. –  Nick Alexeev Mar 7 at 18:50
    
@hillsons Do you have a particular battery in mind (if so, a link to the datasheet wouldn't hurt)? Or, are you making a mental experiment with a hypothetical battery? –  Nick Alexeev Mar 7 at 19:07
    
I'm just sticking to hypotheticals this time. For the purposes of this question let's go with 2Wh –  hillsons Mar 7 at 19:18
    
'a battery with a 2 W capacity' is a strange notion. Are you sure you got the unit right? Batteries a commonly rated in current * time, for instance mAH or AH. –  Wouter van Ooijen Mar 8 at 0:43

2 Answers 2

up vote 4 down vote accepted

"If I want to charge a battery with a 2 watt capacity, how long is it going to take me if I'm using a power source with a continuous output of 2 watts?"

There is no way to tell. The maximum instantaneous power output (2 W in your case) doesn't tell us how much total energy the battery can hold. For example, if this battery can only sustain this 2 W output for 15 minutes before it goes dead, then it can hold 1/2 Watt-hours, which is 1.8 kJ. If it can sustain 2 W output for 10 hours, then it can hold 20 Watt-hours, or 72 kJ.

You are charging the battery at 2 W, which is the same as saying you are transferring 2 J of energy into the battery every second. Obviously it will take a lot longer to transfer 72 kJ of energy at 2 J/s than it will take to transfer 1.8 kJ at 2 J/s.

On top of that, batteries have inefficiencies. If this battery is 75% efficient, for example, then you need to give it 1/75% = 1.33 times more energy during charging than it can ultimately hold and return to you during discharging.

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If I want to charge a battery with a 2 watt capacity, how long is it going to take me if I'm using a power source with a continuous output of 2 watts?

If the power source of 2W has a terminal voltage of 1.5V it is capable of delivering 1.333A. If the battery has a terminal voltage of 1.5V and is connected to the power source, no current and no power will be delivered to the battery because there is no potential difference to drive any current.

It's all about volts and amps and not really about power. But....if the power source were regarded as a "true and perfect" power source, it would deliver 2W into an open circuit or a short circuit and that doesn't make sense in the real world does it?

Neither does it make sense when we talk about a voltage source connected to a short circuit or a current source connected to an open circuit unless we think about the practical limitations.

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