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?

 

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.

 

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

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

 

So then energy will be -3.99 Joules?