Use a two transistor multivibrator as your AC source. 4mS = 1000/4 =250 ohms but K = 5 therefore the resistance is 50 ohms?, So you are measuring between 50 and 30 ohms.
The easiest way to do it is to use a Wheatstone bridge. Use 2 X 60 ohm resistors for one arm, the cell and a calibrated 100 potentiometer for the other. Use an opamp as a differential amplifier/ rectifier, powering a LED which goes out at balance. Or just measure the voltage across the cell, feed to an opamp rectifier which feeds a meter which you need to calibrate.
Frank