# Find t (in seconds)

• Aug 4th 2008, 02:29 AM
magentarita
Find t (in seconds)
The equation governing the amount of current I (in amperes) after time t (in seconds) in a simple RL circuit consisting of a resistance R (in ohms), an inductance L (in henrys) and an electromotive force E (in volts) is given by

I = (E/R)[1 - e^(-(R/L))t]

If E = 12 volts, R = 10 ohms and L = 5 henrys, how long does it take to obtain a current of 0.5 ampere?
• Aug 4th 2008, 02:49 AM
mr fantastic
Quote:

Originally Posted by Air
Rearrange to make time the subject and then substitute the values give.

Rearranging the equation for time, I obtained:
$\displaystyle t = \frac{E-IR}{e^{-\frac{R}{L}}E}$

Unfortunately Air, despite appearances to the contrary, the expression is meant to be $\displaystyle I = \frac{E}{R}\left[1 - e^{-(R/L)t}\right]$.

Since my algebra is terrible, I'd substitute the given values first and then re-arrange. I find it much easier to manipulate concrete numbers.

Do this and you should be able to get to

$\displaystyle \frac{5}{12} = 1 - e^{-2t}$.

From here the path leading to t shouldn't be too slippery.
• Aug 4th 2008, 05:21 AM
magentarita
Thanks
I thank you for taking me half way.