  We report on the development of a capacitance measuring system which allows
measurements of capacitance in pulsed magnetic fields up to 61~T. By using this
system, magnetic-field responses of various physical quantities such
magnetostriction, magnetic-field-induced change in complex dielectric constant,
and magneto-caloric effect can be investigated in pulsed-magnetic-field
conditions. Here, we examine the validity of our system for investigations of
these magnetic-field-induced phenomena in pulse magnets. For the
magnetostriction measurement, magnetostriction of a specimen can be measured
through a change in the capacitance between two aligned electrodes glued on the
specimen and a dilatometer. We demonstrate a precise detection of valley
polarization in semimetallic bismuth through a magnetostriction signal with a
resolution better than 10$^{-6}$ of the relative length change. For the
magnetic-field-induced change in complex dielectric constant, we successfully
observed clear dielectric anomalies accompanied by magnetic/magnetoelectric
phase transitions in multiferroic Pb(TiO)Cu$_4$(PO$_4$)$_4$. For the
measurement of magneto-caloric effect, a magnetic-field-induced change in
sample temperature was verified for Gd$_3$Ga$_5$O$_{12}$ with a capacitance
thermometer made of a non-magnetic ferroelectric compound
KTa$_{1-x}$Nb$_x$O$_3$ ($x$ = 0.02) whose capacitance is nearly
field-independent. These results show that our capacitance measuring system is
a promising tool to study various magnetic-field-induced phenomena which have
been difficult to detect in pulsed magnetic fields.
