  In this study, we develop experimental apparatus for contactless electrical
conductivity measurements under pulsed high magnetic fields over 100 T using a
self-resonant-type high-frequency circuit. The resonant power spectra were
numerically analyzed, and the conducted simulations showed that the apparatus
is optimal for electrical conductivity measurements of materials with high
electrical conductivity. The newly developed instruments were applied to a
high-temperature cuprate superconductor La$_{2-x}$Sr$_x$CuO$_4$ to show
conductivity changes in magnetic fields up to 102 T with a good signal-to-noise
ratio. The upper critical field was determined with high accuracy.
