RC Circuit
30 volt source
0.1 μf capacitor
Capacitor charges to 22 volts after 65μs

The only unknown is the Resistance Value

I'm fairly certain that the formula for Capacitor Voltage is the one to use to solve for R

But i cannot recall how to manipulate the formula

Formula:
Vcap = Vsource(1-e(-t/RC))

The solution is 492Ω, but the closest i get is 477Ω

22/30 * (0.1μs/65μs) = 476.666Ω

 

If you correctly substitute the values into the equation, re-arrange and solve you will get the right answer. Since you have an exponential term involved you are going to have to find a natural logarithm somewhere in the solution process.

Vcap=Vsource(1-exp(-t/RC))

22=30*(1-exp(-(65e-6)/(R*0.1e-6)))

R is the unknown.

It might be preferable (for me anyway) to rearrange the equation first to obtain R as the subject and then make the known value substitutions.

 

That's exactly what I'm trying to do (the 477 answer is just throwing other value together basically) but i cannot remember how to re-arrange that formula to isolate for R

 

V\(_{c}\) = V\(_{s}\)(1-e\(^{-t/RC}\))

e\(^{-t/RC}\) = 1-V\(_{c}\)/V\(_{s}\)

-t/RC = ln(1-V\(_{c}\)/V\(_{s}\))

R = -t/C*ln(1-V\(_{c}\)/V\(_{s}\))

 

Thanks Alex, you're the man...

it's been 2 years since I've done that kind of circuit analysis.