I for one appreciate the quality of your post and the fact that you are honest with the fact that this is an assigment. Thank you for the respect, absence of txt speak.
As I understand you wish to mesure the value of a capacitor by mesuring the time it takes for it to reach a certain voltage from empty.
If I remember well, in a capacitor-resistor in series dipole connected to a supply of potential difference Us, the capacitor voltage evolves in Uc=Us(1-e^(-RCt))
If you start from Uc = 0 (which you should be thinking about as you are most probably not), and trigger the pic at Uc = .95Us, this should take roughly 5RC s to get there, hence, if you count a time Tc on the pic, you should get C = T/(5R). You can then happily display that on the 7 segment.
2 pitfalls i can think about :
- The actual resistance from the chaging leg of the circuit has to encompass the resistance of the charging source of the circuit, including possible current limiting if it is from a mcu pin, ie you should probably use an external mosfet with low OR controlled/well specified on resistance.
- The pic is going to detect low before the capacitor is actually empty, hence you shall wait some more, or possibly use some low resistance path to ground to discharge the capacitor to zero in a short time once low is detected.