I have just started reading the "Basic Engineering Circuit Analysis" book, in the book's chapter 1 problems, I'm trying to resolve the following problem:

My try:

\(w\,(t)=p\,t\)

\(w\,(t)=v\,i\,t

w\,(t)=v\,\left(\frac{q}{t}\right)\,t

w\,(t)=v\,\left(\frac{q}{\cancel{t}}\right)\,\cancel{t}

w\,(t)=v\,q

w\,(t)=\int_{0}^{0.05} \left(120e^{-2t}\right)\,\left(\dfrac {-30e^{-4t}}{1000}\right)\,dt \)(division by 1000 for converting mC to C)

\(w\,(t)=-0.15 J \)

I feel something wrong with my solution. What is that?

 

Why do you feel there is something wrong?

Before you started, you should have done a couple of estimates to sanity check your answer against.

One would have been to ask what sign the final answer should have.

Another would have been to get a bounding value for the answer. Since both the current and voltage are decaying, they will be at their peak at the start. So assume that they are constant at those initial values. How much energy is delivered in 50 ms under those conditions?

As a general rule, you answers should be given to three sig figs and, from a practical standpoint, a leading one is often not counted for this purpose.

Finally, you should always carry your units throughout your work. Always. Then you don't have to make side notes about why you are dividing by 1000. Also, because the problem didn't properly provide units, it is somewhat ambiguous. Is the t in the exponentials supposed to be in seconds, or in ms since that is what the interval is specified in. Had the author done it properly, it wouldn't have mattered because all the information would have been right there.

 

Why do you feel there is something wrong?

Before you started, you should have done a couple of estimates to sanity check your answer against.

One would have been to ask what sign the final answer should have.

Another would have been to get a bounding value for the answer. Since both the current and voltage are decaying, they will be at their peak at the start. So assume that they are constant at those initial values. How much energy is delivered in 50 ms under those conditions?

As a general rule, you answers should be given to three sig figs and, from a practical standpoint, a leading one is often not counted for this purpose.

Finally, you should always carry your units throughout your work. Always. Then you don't have to make side notes about why you are dividing by 1000. Also, because the problem didn't properly provide units, it is somewhat ambiguous. Is the t in the exponentials supposed to be in seconds, or in ms since that is what the interval is specified in. Had the author done it properly, it wouldn't have mattered because all the information would have been right there.

Grateful for you WBahn and thanks for the helpful tips.

 

great point