PLEASE HELP with Capacitor!!

About 4(f)(II), I used to V=V0e^(-t/RC) equation to find the value of R as 137ohm but it is wrong

Can somebody please explain to me how we use use proportion equation of T=RC and original R value from graph?

even so 137 is still closer to 150 than it is to 100. why didn't you go for 150 anyway?

Cuz when R is larger, T is also larger. I was thinking if R is 150, time needed will be more than 12s.

Well you already worked out from the experimental data that the real circuit was about 10% quicker than the theoretical calculation... so for a new time interval making R 10% greater, i.e. 10% slower than the theoretical calculation should get you close.
137+13.7=150.7
----

anyway


V₀ = 12 V
V = 5 V
C= 100x10^-6F

new value for time elapsed t=12 s

ln V - ln V₀ = -t/RC

get everything that's not changed onto the same side of the equals sign

C (ln V - ln V₀) = -t/R

what this means is that if everything else is held constant then -t/R is constant ratio... so it'll be the same for the new value of R that makes t=12s as it was for the old value of R when t was measured at 17.5 s

t_old/R_old=t_new/R_new

17.5/(220x10³)=12/R_new

12/(17.5/(220x10³))=R
= 220x10³ * (12/17.5)

Thanks!
So we should check whether the experimental value matches the theoretical one before we apply an equation to calculate the new value?

in this case yes because it seems to be asking us what the designer will choose to make t=5 based on information from the experiment rather than calculate a theoretical value.
calculating a %age difference between expected and actual was an earlier part of the question (I looked up the paper to see the the whole question) , if you've worked through the question in order it could have been a clue.