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Although the current is double it uses 4 times the power.
A hair drier designed to run on 110volt at 450W would have a resistance of 110²/450 = 26 ohms plugged into 230volt then 230²/26 = 2Kw so with 4 times the power something has to go pop very quickly. (1967.355W is nearly 2Kw and by time you allow for the fact that the element is coiled and the frequency has dropped from 60 to 50Hz it would likely be 2Kw) also just to compound the problem even further the fan will also be going slower.
But if you got a UK 2Kw electric heater and connected this in series with the 450W USA hair drier the hair drier would work OK. So the work required to overcome the voltage is not hard to correct but if we take a clock designed to work in USA to get that to work in the UK would be a lot harder so the frequency is a much bigger problem than the voltage.
A hair drier designed to run on 110volt at 450W would have a resistance of 110²/450 = 26 ohms plugged into 230volt then 230²/26 = 2Kw so with 4 times the power something has to go pop very quickly. (1967.355W is nearly 2Kw and by time you allow for the fact that the element is coiled and the frequency has dropped from 60 to 50Hz it would likely be 2Kw) also just to compound the problem even further the fan will also be going slower.
But if you got a UK 2Kw electric heater and connected this in series with the 450W USA hair drier the hair drier would work OK. So the work required to overcome the voltage is not hard to correct but if we take a clock designed to work in USA to get that to work in the UK would be a lot harder so the frequency is a much bigger problem than the voltage.