This study investigated the frequency properties of a flexible printed circuit (FPC) coil and applied it to detect conductivity change of non-ferromagnetic metal materials. Theoretical analysis and measurements showed that the coil's resistance and inductance are almost frequency-invariant in a particular frequency range; the coil circuit resonates at its self-resonant frequency. With no concern for its thickness, the conductivity of a test object can be measured with high sensitivity and accuracy by using the coil in its frequency-invariant range, based on the "same ωσ, same impedance"principle. In the case that the influence of thickness has to be eliminated, the variation of conductivity can be sensitively detected by using the coil's resonant properties. The proposed methods have been verified with measurement of standard test pieces whose conductivities were given in advance, and applied to detect conductivity change of deteriorated tube.