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Does the power axis in power-time curve in 'power statistics' application denotes to watt per hour ?

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If you mean this curve

enter image description here

Then no. It's not very useful to think in terms of watts per hour. Power measured in watts is an instantaneous value and is nothing to with time. It is useful to think in terms of watt hours however.

A watt hour is is the energy that would be consumed if your computer consumed 1 watt continuously for 1 hour (or 2 watts for half an hour). You electricity bill is based on the number of watt hours consumed.

On my system however I can only see the power into or out of the battery and not the power being taken from ac supply.

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