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The number you calculate is proportional to the flow rate you put in, so a ten times faster flow rate will require ten times more electrical power, so if you do the same calculation with a flow rate closer to what you'd get from a fountain, you'll probably get a lot closer to the right order of magnitude. This calculation is actually the right way to ...

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The wiki article has a lucid calculation of what you are asking. Notice that this is the incident power, and somewhwere the book must say per meter square on the target. Incident and absorbed are two different concepts. The incident/incoming radiation is computed at the location of the earth, so it depends only on the parameters of the sun and the ...

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What is the point of batteries? Obviously higher W will drain them faster. If question is wattage -> luminocity function then I think that there will be two components. One is that every watt is converted into a lumen (683 lm/W, to be exact according to Wikipedia). It is like $E=mc^2$: more mass = more energy. They are equivalent. So more power <=> more ...

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The bulb rated 500 W is doing more work per unit time, which implies that it is either emitting more light or just using up the energy to generate more heat. If both the bulbs have the same efficiency then it follows that the higher wattage bulb shines brighter.

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For a given circuit in a given technology, power increases at a rate proportional to $f^3$ or worse. You can see by looking at the graph in @Martin Thompson's answer that power is superlinear in frequency. $P=c V^2 f + P_S$ is correct, but only superficially so because $f$ and $P_S$ are functions of $V$ and $V_{th}$ (the threshold voltage.) In practice ...

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