The heat produced in a resistor by an AC curr | vedclass

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(C) The heat produced by an $AC$ current in a resistor $R$ over time $t$ is given by $H_{AC} = I_{rms}^2 Rt$.The heat produced by a $DC$ current $I_{D

Vedclass · Accepted Answer

$3.46$

Vedclass · Answer

(C) The heat produced by an $AC$ current in a resistor $R$ over time $t$ is given by $H_{AC} = I_{rms}^2 Rt$.The heat produced by a $DC$ current $I_{DC} = 2 \, A$ in the same resistor $R$ over the same time $t$ is $H_{DC} = I_{DC}^2 Rt$.According to the problem,$H_{AC} = 3 	imes H_{DC}$.Substituting the formulas: $I_{rms}^2 Rt = 3 	imes (2^2) Rt$.Canceling $R$ and $t$ from both sides: $I_{rms}^2 = 3 	imes 4 = 12$.Therefore,$I_{rms} = \sqrt{12} = 2\sqrt{3} \approx 3.46 \, A$.

The heat produced in a resistor by an $AC$ current is three times the heat produced by a $2 \, A$ $DC$ current. What is the $rms$ value of the $AC$ current in $A$?

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