What must its resistance be?

Question

A camera's flash is powered by a 5.00×10−4 F capacitor. When the capacitor is fully discharged, It takes 2.00 seconds to get 99.0% recharged. A resistor is in series with the capacitor. What must its resistance be?

Answer 1

It takes 5 RC time constants to get to a 99% value (that is something I just have memorized, but the derivation is below)

2 seconds = 5 * R * 5.00*10^-4

BUT... since that 99% is 99.0% (3 decimal places), it won't be exactly 5 time constants, it will be 4.60 time constants

2 seconds = 4.605 * R * C


derivation:
0.993 = 1 - e^-5
0.990 = 1 - e^-4.60517

.

Answer 2

99% is considered 5 time constants...

With that, you have all the info you need.