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Examining the following graph, I am trying to understand the power plot. The power appears to take on a negative value when the current changes direction or the voltage changes polarity. Negative power does not make sense to me. In a proper representation of the power curve shouldn't the power remain above the dotted line? Additionally, since the power is a product of voltage and current, I would think that the power plot should be a maximum value during where the plots of the voltage and current intersect, and should be greater in magnitude the the plots of the voltage and current.

enter image description here

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Now to answer your question, first I want to point out what $V$ and $I$ should be representing. The negative values of these functions represents the change in the direction of either the electric field $E$, or the current density $J$, which is a vector with a magnitude of current per unit volume.

Now if you think about these things in this way, then negative power starts making sense, as it just means, that the power flux (the propagation of energy) direction reverses at some point and starts travelling to the opposite direction than the one you arbitrarily define.

Hope this is clear enough.

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This does clear it up to some degree. However I am under the impression that power is a scalar quantity. I am also somewhat unclear as to whether voltage is scaler or vector quantity. Does voltage have a direction? or just a polarity? and are those two things directly related? – Kurt Mar 23 '13 at 19:20
@Kurt Power isn't necessarily a scalar quantity. Power represents the rate at which work is done. Recall that work can be either positive or negative, depending on whether energy is being added or removed from a system. For example, how much power does a standard light bulb generate? It generates -60 watts, meaning that it consumes 60 watts. – Ataraxia Mar 23 '13 at 19:42

Negative power does not make sense to me

The sign of the power associated with a circuit element tells you whether the element is absorbing or supplying power.

By the passive sign convention, the reference direction for the current is into the positive reference terminal. The product of the voltage across and the current through the element is positive when the element is absorbing power and negative if it is supplying power.

enter image description here

For example, an ordinary resistor never supplies power to a circuit so the power associated with a resistor is always positive.

However, a reactive component, such as a capacitor, alternately absorbs and supplies power to an AC circuit; the power is alternately positive and negative.

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Awesome explanation. Thanks. – Kurt Mar 23 '13 at 20:18

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