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I is current, R is resistance
Power = IIR
Energy = Power * seconds
R = (kg/Coulomb^2) * meter^2 / second
II = Coulomb squared per second squared
IIR = Power
IIR = (Coul^2 / sec^2) * (kg / Coul^2) * (meter^2 / second)
The Coulombs cancel out, combine seconds
IIR = kg * (meter^2 / second^3) = Power
II = kg * (meter^2 / second^2) = Energy
Current squared is energy.
QED
Power = IIR
Energy = Power * seconds
R = (kg/Coulomb^2) * meter^2 / second
II = Coulomb squared per second squared
IIR = Power
IIR = (Coul^2 / sec^2) * (kg / Coul^2) * (meter^2 / second)
The Coulombs cancel out, combine seconds
IIR = kg * (meter^2 / second^3) = Power
II = kg * (meter^2 / second^2) = Energy
Current squared is energy.
QED