# Finding Maximum Current Entering A Terminal

1. Sep 23, 2011

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

The expression for the charge entering an upper terminal of a component is:

q = 1/$\alpha^{2}$ - (t/$\alpha$ + 1/$\alpha^{2}$)e$^{-t\alpha}$

Find the maximum value of the current entering the terminal if $\alpha$ = 0.03679 s$^{-1}$

2. Relevant equations

3. The attempt at a solution

Since they gave us the equation for the charge, to find current we simply take the derivative with respect to time of the given equation. I did this and ended up with te$^{-t\alpha}$. This seems to check out just fine. I then realized that they want the maximum value that this derivative can be. So then I went ahead and took the second derivative and tried to set it equal to 0 (since that would be a local max or min). This ended up being very messy and it didn't work out. Is there an easier way to find the maximum current?

2. Sep 23, 2011

### MetalManuel

Let me know if my mathematics is incorrect, but
$\frac{dq^{2}}{d^{2}t}=e^{-t\alpha}-\alpha te^{-t\alpha}=e^{-t\alpha}(1-\alpha t)=0$
$e^{-t\alpha}\neq0$, therefore $1-\alpha t=0$

and $t=\frac{1}{\alpha}$

You can go from there

edit: this is going from your 1st derivative, I haven't checked it myself

3. Sep 23, 2011

### PeterO

Not too comfortable with your first derivative. t appears in two places in the original expression. I think you may have overlooked one??

4. Sep 23, 2011