In a $2-$wire underground cable cut detection system, a reading of $500$ nF was measured between the two wires of the cable at the beginning of a $20$ km cable. If the nominal capacitance for the cable is $100$ nF$/$km$,$ how far is the cut from the detection system?

In another occasion, there was a short circuit in the cable. If the measured value of the resistance between the two wires of the cable at the beginning of the cable was $100,$ how far is the short circuit from the ohmmeter if the cable has $10/$km$?$