1. ## Some basic questions

Hi!

We know from physics that $\displaystyle E = P \cdot t$ , where E is the energy, P the power and t the time.

If we have $\displaystyle P=P(t)$ , that is, power as a function of time, we could integrate this expression from $\displaystyle t_{1} \mbox{ to } t_{2}$ , and get the total energy.

Here is where I am confused.
Which is correct?

$\displaystyle dE=P\cdot dt$

$\displaystyle dE=P'(t)\cdot dt$

Because usually, $\displaystyle \frac{dy}{dx}=y'(x)$ . This looks like the second one.

But i also makes sense to think about $\displaystyle dE$ as some "energy strip" , with height P and width dt.

Kinda want this cleared out.

Thx!

2. Originally Posted by Twig
Hi!

We know from physics that $\displaystyle E = P \cdot t$ , where E is the energy, P the power and t the time.

If we have $\displaystyle P=P(t)$ , that is, power as a function of time, we could integrate this expression from $\displaystyle t_{1} \mbox{ to } t_{2}$ , and get the total energy.

Here is where I am confused.
Which is correct?

$\displaystyle dE=P\cdot dt$

$\displaystyle dE=P'(t)\cdot dt$

Because usually, $\displaystyle \frac{dy}{dx}=y'(x)$ . This looks like the second one.

But i also makes sense to think about $\displaystyle dE$ as some "energy strip" , with height P and width dt.

Kinda want this cleared out.

Thx!
dE/dt = E', not P'.

$\displaystyle dE = P \cdot dt$ is the correct expression.

3. Yes of course what was I thinking

Thanks man!