Why is that considered when the voltage is more than a certain point?
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The designations high, medium and low voltage are arbitrary. Just numbers chosen and agreed upon. With respect to transmitted power Iow voltage is service voltage of 600 volts or less Medium voltage is between 600 volts and 50 kilovolts. High voltage is above 50 kilovolts
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Well this is relative to what you're working with, but 600 volts is usually a high voltage. Your home (in the US) is 120 volts, so I would call that typical. Anything above that would be referred to as high voltage as in higher than normal, e.g. 240 volts. But that does not mean that a normal 120v current is safe or should be handled without caution.
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It depends on the context. For utlity power generation and distribution it would be considered low voltage.