Beginner question - Find out the charge, power and energy

[sonutulsiani]

Hello, this might be an easy question but it's confusing for me. So please help.

Current flowing through an element is i(t)= 2e^(-t) and voltage across that conductor is v(t)= 2 (di/dt). Find out the charge is delivered to the element and power and energy consumed by the element in between 0 to 3 seconds.

I got charge as 1.9 C

I power as -8 e^(-2t) but when I asked my professor, he said I don't have to substitute t=3 in this.

But in energy he said i have to substitute t=3 in e = p*t.

What will be the final answers and why don't we substitute t=3 in power but we do in energy?

[t_n_k]

The (instantaneous) power is defined by the general relationship

p(t)=v(t)*i(t)

and as such has a time varying value.

We get so used to talking about power as if it were a constant value (in a "time-varying" circuit at "steady-state" condition - figure that one out!) that we sometimes lose sight of the reality of the situation.

Nett energy over any given time interval is the integral of p(t) over the interval.

[sonutulsiani]

So you mean power is -8e^(-2t)

But energy will be integral of -8e^(-2t) between 0 and 3?

[sonutulsiani]

So then energy will be -3.99 Joules?