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I'm reading electric power from the book "Fundamentals of physics textbook by Robert Resnick" and I have a question about the interpretation of the text. First it says "The principle of conservation of energy tells us that the decrease in electric potential energy from a to b is accompanied by a transfer of energy to some other form. The power P associated with that transfer is the rate of transfer dU/dt..". Then in the next paragraph it says:

"Moreover, this power P is also the rate at which energy is transferred from the battery to the unspecified device".

Is it saying the same thing twice? What does this second paragraph add?

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Is it saying the same thing twice?

No. The second paragraph adds the source of the energy supplied to the device.

The first statement accounts for what happens to the electrical potential energy furnished to the device, which depends on the device. The second statement accounts for the source of the electrical potential energy delivered to the device, namely the power delivered by the battery.

Hope this helps.

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  • $\begingroup$ Just one more. The energy transfer Resnick talks about in the first paragraph is a transfer of electrical potential energy to another form (depending on the device). Whereas the transfer he talks about in the second paragraph is more general, since it encompasses the source of potential difference. Is this correct? $\endgroup$
    – Gabriel Diez
    Commented Aug 8 at 13:31
  • $\begingroup$ @GabrielDiez Essentially yes. In the first paragraph he talks about what happens to the electrical potential energy delivered to the device whereas in the second paragraph he talks about the source of the electrical potential energy (battery) delivered to the device. The overarching theme is conservation of energy. To complete the considerations I would also talk about conversion of chemical potential energy to electrical potential energy in the battery. Ultimately it is that chemical potential energy that is converted to the various energy forms in the device. $\endgroup$
    – Bob D
    Commented Aug 8 at 13:44
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A voltmeter connected between a and b (see diagram) would indicate a potential difference between these points, that is a loss of electrical potential energy per unit (positive) charge going from a to b (or negative charge going from b to a). The voltmeter doesn't tell us anything about the source of the electrical potential energy. In fact there is an energy transfer from chemical to electrical potential as charge passes through the battery. This is, strictly speaking, an additional fact, not deducible from Resnick's previous paragraph.

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  • $\begingroup$ Would the downvoter please explain why the downvote was given? $\endgroup$
    – Philip Wood
    Commented Aug 7 at 21:32
  • $\begingroup$ I don't see you answering the question which was: "Is it saying the same thing twice? What does this second paragraph add?" For example you mention transfer from Chemical to electrical etc this is not even in paragraph 2 (the last paragraph). $\endgroup$
    – user417360
    Commented Aug 7 at 21:44
  • $\begingroup$ Thanks for replying. Admittedly Resnick's last para didn't mention the nature of the energy transfer inside the battery, but it did mention – for the first time – the battery as source of the electric potential energy, therefore Resnick is not saying the same thing twice. I think this does answer the question! $\endgroup$
    – Philip Wood
    Commented Aug 7 at 22:04
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    $\begingroup$ Yes I see what's happening now. In reality there are four paragraphs. The OP quotes from paragraph 4 and asks "Is it saying the same thing twice? What does this second paragraph add?" I assumed he is asking about paragraph 4 because the quote he gives is from paragraph 4. You assumed he is asking about paragraph 2. By the way you are talking about a voltmeter - nowhere is a voltmeter mentioned in the original text, it just gives a potential difference of magnitude V - and that's sufficient. $\endgroup$
    – user417360
    Commented Aug 7 at 22:26
  • $\begingroup$ I brought in a voltmeter to re-inforce the idea of potential difference. I didn't imply that Resnick had mentioned a voltmeter. $\endgroup$
    – Philip Wood
    Commented Aug 8 at 6:47
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Yes the first paragraph is mostly specifically about how energy is being transferred via the wires to the load (a b). It talks about charge transfer and then says the energy (power) transferred is P=iV This is Watts = Amps x Volts.

The second paragraph is going on to say that this energy (power) in Watts is being transferred to the unspecified load and goes into whatever the device is or is doing.

So the second paragraph is not about the wires but about the energy getting from the battery to some device - motor, lamp, bell, Lithium cell etc.

The text sounds old (the book was originally published in 1960), this part is very verbose and long winded (like my answer) and overly rigorous. Keep in mind that in the early days of electricity these things were far from obvious to people generally, also it seemed like magic back then and worthy of detailed explanation.

It is also slightly confusing because that line of thought would lead onto power consumption in Watt Seconds or kWh.

So there is voltage in Volts, charge Q in Coulombs, current in Amps, energy in Joules, power in Watts and power consumption in kWh to keep in mind.

Hope that helps your understanding.

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