An electrical heater is connected Turn by turn to DC and an AC source of the same voltage will the rate of heat production be same in the two case

Dear student, 

The element of an heater is an inductor of inductance L (say) besides the resistance R.For, AC current, effective resistance=R2+ωL2For, DC current, effective resistance=R
So, for same voltage DC source will produce more heat.

Regards.

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