Rearranging formula using logarithms

[Mr_Mole]

Homework Statement

I have a homework where I need to use logarithms to make an unknown the subject of a given formula. I know the answer I need (different values in the formula till one worked) but I can’t show how it’s done using logs.

If the flow of current (i), Amperes, in a capacitor at time (t), seconds, increases at an exponential according to the equation below:
i=6.7(1-e^(-t⁄RC) )
The resistance of the circuit is 28kΩ and the capacitance is 15µF.
Calculate the current after 750ms
Calculate the time for the current to reach 5A.

Relevant Equations

i=6.7(1-e^(-t⁄RC) )

My attempt that doesn’t work. t=-RC ln(1-I/6.7)

 

[YouAreAwesome]

Your "attempt that doesn't work" looks correct to me. To show why this is true via logarithms you'll need to use the idea that ln(e^x)=x for x>0. In other words, make e^x the subject of the equation and then take the natural log of both sides.

 

[DaveE]

It looks good to me also. Why do you think it's not correct?

 

[malawi_glenn]

What is the answer supposed to be?

 

[Mr_Mole]

It looks good to me also. Why do you think it's not correct?

Because when I put values into it then I get the wrong answer. Using the information given in the question I get an answer of 5.576A for the first part. Putting that into the rearranged formula gives me a t value of 326milliseconds instead of 750milliseconds.

 

[YouAreAwesome]

Because when I put values into it then I get the wrong answer. Using the information given in the question I get an answer of 5.576A for the first part. Putting that into the rearranged formula gives me a t value of 326milliseconds instead of 750milliseconds.

How are you getting 326ms?

 

[Mr_Mole]

It looks good to me also. Why do you think it's not correct?

Homework Statement: I have a homework where I need to use logarithms to make an unknown the subject of a given formula. I know the answer I need (different values in the formula till one worked) but I can’t show how it’s done using logs.

If the flow of current (i), Amperes, in a capacitor at time (t), seconds, increases at an exponential according to the equation below:
i=6.7(1-e^(-t⁄RC) )
The resistance of the circuit is 28kΩ and the capacitance is 15µF.
Calculate the current after 750ms
Calculate the time for the current to reach 5A.
Relevant Equations: i=6.7(1-e^(-t⁄RC) )

My attempt that doesn’t work. t=-RC ln(1-I/6.7)

I’m not expecting the current to be 5A at 750ms. When rearranged to make t the subject, I would expect t to be 750ms when I input the current obtained when i is the subject. That was around 5.6A. I’m getting 325ms out which led me to believe it was incorrect. This aspect of maths baffles me hence how I ended up here relying on the kindness of helpful strangers with bigger brains than I.

 

[YouAreAwesome]

I’m not expecting the current to be 5A at 750ms. When rearranged to make t the subject, I would expect t to be 750ms when I input the current obtained when i is the subject. That was around 5.6A. I’m getting 325ms out which led me to believe it was incorrect. This aspect of maths baffles me hence how I ended up here relying on the kindness of helpful strangers with bigger brains than I.

Can you explain how you are getting times of 325ms or 326ms?

 

[BvU]

I’m getting 325ms out

One of the more frequent mishaps: you used LOG on your calculator instead of LN



$\$

 

[Mr_Mole]

Can you explain how you are getting times of 325ms or 326ms?

I input the values into the rearranged equation. Using the same values given and the original answer I would expect to get the original i value returned to prove I had rearranged correctly. Unless I’m missing a step somewhere in the process and doing the rearranged equation incorrectly.

 

[Mr_Mole]

One of the more frequent mishaps: you used LOG on your calculator instead of LN



$\$

We have a winner! If only the maths tutor had explained that. No mention of an ln button. It comes out correct now. You are my hero! It was driving me mad last night as I couldn’t see the error. I will sleep well tonight!

 

[Mr_Mole]

I input the values into the rearranged equation. Using the same values given and the original answer I would expect to get the original i value returned to prove I had rearranged correctly. Unless I’m missing a step somewhere in the process and doing the rearranged equation incorrectly.

Thank you for helping. It’s been pointed out I didn’t know the existence of the ln button. I blame the tutor for not explain that one.