# Elementary circuit theory question

1. Sep 4, 2008

### 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 havent the slightest idea how to get them.

2. Sep 4, 2008

### jmckennon

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

3. Sep 4, 2008

### Redbelly98

Staff Emeritus
What is the power as a function of time?

4. Sep 4, 2008

### jmckennon

1. The problem statement, all variables and given/known data

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 havent the slightest idea how to get them.

2. Relevant equations

p=vi

p=-vi

3. 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.

5. Sep 4, 2008

### jmckennon

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

6. Sep 4, 2008

### chroot

Staff Emeritus
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

7. Sep 4, 2008

### chroot

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

- Warren

8. Sep 4, 2008

### 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.

9. Sep 4, 2008

### chroot

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

- Warren

10. Sep 4, 2008

### jmckennon

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

11. Sep 4, 2008

### Redbelly98

Staff Emeritus
Also: have you ever taken a calculus class?

12. Sep 4, 2008

### 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.

13. Sep 4, 2008

### Redbelly98

Staff Emeritus
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 ...