Electrical conductivity measurement using an eddy current sensor requires measuring the absolute change in the impedance of the sensing coil. There have been many different attempts at this by using phase sensing circuits, utilizing impedance analyzers etc. This work utilizes two different oscillator circuit (LC oscillator using an unbuffered inverter and Relaxation Oscillator) to determine the change in impedance of the coil. The LC oscillator is designed in such a way that the circuit is insensitive to change in the series resistance of the sensing coil and hence, only a function of the inductance of the coil. Once the inductance of the coil is determined, a relaxation oscillator is used in an operating region in which the output frequency is a strong function of the series resistance of the coil. This switched oscillator circuit technique is used to determine the impedance of a cryogenic sensing coil at 295 K and 77 K with a Niobium (Nb) target kept at specific distance. Experimental data is compared with that of an impedance analyzer circuit and measurement errors are presented.