Struggling to re-arrange exponential equation

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The discussion revolves around rearranging the exponential equation i = 12.5(1-e-t/CR) to solve for time (t) after calculating current. The user successfully calculated current but struggled with the rearrangement needed to find the time to reach 10A, encountering errors and confusion with negative signs in the process. They attempted multiple methods, including treating the exponential term as a variable, but still faced issues with their calculations. Ultimately, they received guidance indicating a negative sign was missing in their rearrangement, which helped clarify the solution. The user plans to revisit their notes for further assistance.
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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 doesn't 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 as well but that didnt work either!
 
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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.
 
I can only remember one of the ways i did it, as said i forgot to bring my paper work with me! :rolleyes:

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 I am going to go and give that a go, from the notes I've found I've done it completely wrong.
 
That's correct.

edit: Never mind, Char. Limit is right. You dropped a negative sign in front of your exponential
 
Rusty789 said:
I can only remember one of the ways i did it, as said i forgot to bring my paper work with me! :rolleyes:

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 I am 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.
 
I've done this now, thanks for the help.
 
I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
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