# How is the equation for Power [U'] derived?

1. Aug 13, 2009

### Ognerok

1. The problem statement, all variables and given/known data

While going through a basic electrical engineering overview, I came across the equation U = QV, which is defined to be electrical energy. For Power, which is explained in the next section, P is basically the derivative of U = QV. I tried following the derivation myself, but for some reason, what I got was different from the book.

2. Relevant equations

U= QV

q = -1.6x10^-19 Coulombs ( basically a constant)

The derivative of this turned out to be d/dt = V*d[Q]/dt. My question is HOW.

3. The attempt at a solution

P = d/dt = Q * d[v]/dt; treated Q as a constant, but this doesn't line up. My Calculus must be rusty. Anyway, the full statement from the book:

P = U'= V*Q' = VI= v^2/R = I^2*R

-Thanks.

2. Aug 13, 2009

### rl.bhat

Power is the rate of work done against the opposition to the flow of charges in the conductor. While doing so the voltage across the conductor is constant.
So P = U' = V*dQ/dt.

3. Aug 13, 2009

### Ognerok

That makes more sense. But...I thought Q itself was just a constant, you know, an electron's charge...it must be Q in the sense that Q = u/V? :)

4. Aug 13, 2009

### rl.bhat

It is different. It is the energy acquired by a charge when it is accelerated the a potential difference V. It is nothing to do with the power dissipated in a resistance.