Elementary circuit theory question

[jmckennon]

it's only the second day of class but my professor assigned some problems that are those weird ones that neither he nor the book even discusses, I have tried several different methods including parametric graphing, integrating the functions, deriving the function, but to not even the slightest avail.

the question is

The voltage and current at the terminals of the circuit element are zero for t<0 and t>3s. In the interval between 0 and 3 s the expressions are v=t(3-t)V i=6-(4*t)

the book tells the answers as being t=.634s where the power is delivered at its maximum and 2.366s where it is extracted at its maximum but i haven't the slightest idea how to get them.

 

[jmckennon]

ahh sorry for posting this in the wrong forum, I am extremely new on here

 

[Redbelly98]

What is the power as a function of time?

 

[jmckennon]

Homework Statement

t's only the second day of class but my professor assigned some problems that are those weird ones that neither he nor the book even discusses, I have tried several different methods including parametric graphing, integrating the functions, deriving the function, but to not even the slightest avail.

the question is

The voltage and current at the terminals of the circuit element are zero for t<0 and t>3s. In the interval between 0 and 3 s the expressions are v=t(3-t)V i=6-(4*t)

the book tells the answers as being t=.634s where the power is delivered at its maximum and 2.366s where it is extracted at its maximum but i haven't the slightest idea how to get them.

Homework Equations

p=vi

p=-vi

The Attempt at a Solution

I tried integrating the two functions from 0 to 3 and got 9/2 which is 4.5W. when using the book's answer the result is 4.964, and all my other attempts are no where near correct.

 

[jmckennon]

well i know 1W is 1 J/s, and 1V is 1 J/Q and 1A= 1Q/s

 

[chroot]

Power is an instantaneous quantity -- you don't need to integrate anything. If you integrate power over time, you get energy, which is not what you're looking for.

You have v(t) and i(t), so simply multiply them to find p(t):

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

- Warren

 

[chroot]

Both threads have been merged. Please don't post the same question multiple times.

- Warren

 

[jmckennon]

i realized that after i posted it in the EE forum.

i understand how to get power as a function of time. My question is that i don't understand how the book got t= .634s as the time maximum power is delivered and t= 2.366s as the time max power is extracted.

 

[chroot]

If you look at a plot of p(t), and find its maximum and minimum, do you get the correct values of t?

- Warren

 

[jmckennon]

I haven't even tried that I'll go try that now!

 

[Redbelly98]

Also: have you ever taken a calculus class?

 

[jmckennon]

yes, i have. i have been trying to tie together the voltage and current equations with parametric graphing but i still don't see where those numbers the book got comes from. i mean i see that the power would be at it's maximum value, but i don't know how to show the work for it.

 

[Redbelly98]

In first semester calculus, you are taught how to find the maximum and minimum of a function. Do you remember? It involves taking the derivative ...