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The physical processes that occur during the initial stages of nanosecond explosion of thin wires play an important role in the development of plasma for nanoparticle preparation. The transition of the wire material from the condensed state to conducting plasma has not yet been fully understood. In this paper, underwater electrical explosions of copper wires were investigated with pulsed voltage in the timescale of a few microseconds. A self-integrating Rogowski coil and a voltage divider were used for the measurements of the current and the voltage on the wire load, respectively. The current rise rate was adjusted by changing the circuit parameters, including the discharge voltage and circuit inductance, and the copper wire properties consisting of the length and the diameter. The effect of the current rise rate on the phase transitions involving melting from solid to liquid and vaporization from superheated liquid to the vapor-drop mixture was obtained by the analysis of the current and voltage waveforms of copper wire explosion. The energy of melting and vaporization was calculated based on experimental waveforms of current and voltage. In addition, the effect of applied voltage, circuit inductance, and the length and diameter of copper wire was acquired on the electrical explosion characteristics of copper wires.