Power dissipation in a conductor is given by the formula ( P = I^2 R ), where ( P ) is power, ( I ) is the electric current, and ( R ) is the resistance. If the electric current is doubled, the new current becomes ( 2I ). Substituting this into the power formula results in ( P' = (2I)^2 R = 4I^2 R ), which shows that the power dissipation increases by a factor of four. Therefore, doubling the current through a constant resistance results in a fourfold increase in power dissipation.
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