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[tex]P = I.Vab[/tex]

where Vab is the potential difference between two terminals of a circuit element.

From my previous studies, I know that.

[tex] P = dW / dt [/tex]

I assume that for a small interval, dt, a single charge q has a small displacement , dx.

Then;

[tex]dW = E q dx[/tex]

where E is magnitude of the electric field.

Hence, from the formula above,

[tex] P = E q dx / dt [/tex]

This is all I could come up with. I want to go on with this idea to prove

[tex] P = I Vab [/tex]

I know I need to substitute dq somewhere (to get I ) , somehow.. Simply replacing q with dq does not seem to work; it leads to an incorrect formula. (I find P = I dV ; I guess, if I do that.)