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thanks bro, I appreciate your replypower dissipation by direct current will be (Irms^2)*R where Irms will be Io
power dissipation by sinusoidal current will be (Irms^2)*R where Irms will be Io/(square root of 2)
[(Io^2) * R] / {[(Io/sqr root of 2)^2]*R}
Io^2*R will be cancelled
inverse of (2) will be left
inverse of 2 will be 2
ratio = 2