# Struggling to re-arrange exponential equation

Rusty789

## Homework Statement

i = 12.5(1-e-t/CR)

Current = i
Resistance = R
Capacitance = C
Time = t

Firstly i had to calculate the current flowing after 0.5s, given a 30k$$\Omega$$ resistance and a 20µF capacitance.. easily done.

Then i had to work out how long it took to reach 10A, so rearranging the formula with natural logs right? So rearranging to work out t.

2. The attempt at a solution

I've done it three times now (different each time just incase i made a stupid error) but forgot to bring my paper work with me but both times I've ended up with a -t and when i put in the numbers it doesnt equal what i'm expecting or the calculator comes up with a math error, from trial and error i'm expecting 966ms or 0.966s. I've done the previous question in which just had letters, so i tried transposing the groups of numbers for letters then working it out after aswell but that didnt work either!

## Answers and Replies

Homework Helper
Gold Member
What is your formula for t after performing the steps to find its formula? Best would be to first treat the exponential term as a variable and solve for it; and then find logarithm of both sides to continue for a formula for t.

Rusty789
I can only remember one of the ways i did it, as said i forgot to bring my paper work with me! :uhh:

I first rearranged it to give me:

(i/12.5)-1 = e-t/CR

Which then i made the left hand side of the equation G to make it easier for me (this may be were i went wrong on this one) i did do it another way without doing this but i can't remember it at all..

lnG = lne-t/CR

lnG = -t/CR

lnG * (CR) = -t

I've found a few more notes online of which look promising, so im going to go and give that a go, from the notes i've found i've done it completely wrong.

tjackson3
That's correct.

edit: Never mind, Char. Limit is right. You dropped a negative sign in front of your exponential

Gold Member
I can only remember one of the ways i did it, as said i forgot to bring my paper work with me! :uhh:

I first rearranged it to give me:

(i/12.5)-1 = e-t/CR

Which then i made the left hand side of the equation G to make it easier for me (this may be were i went wrong on this one) i did do it another way without doing this but i can't remember it at all..

lnG = lne-t/CR

lnG = -t/CR

lnG * (CR) = -t

I've found a few more notes online of which look promising, so im going to go and give that a go, from the notes i've found i've done it completely wrong.

Well there's your problem. There should be a negative sign before that exponential.

Rusty789
I've done this now, thanks for the help.