What is the r.m.s. value of an alternating cu | vedclass

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(C) The heat produced by an alternating current $(ac)$ is given by $H_{ac} = i_{rms}^2Rt$.The heat produced by a direct current $(dc)$ is given by $H_

Vedclass · Accepted Answer

$3.46$

Vedclass · Answer

(C) The heat produced by an alternating current $(ac)$ is given by $H_{ac} = i_{rms}^2Rt$.The heat produced by a direct current $(dc)$ is given by $H_{dc} = i^2Rt$.According to the problem,$H_{ac} = 3 	imes H_{dc}$.Substituting the formulas: $i_{rms}^2Rt = 3 	imes i^2Rt$.Canceling $R$ and $t$ from both sides,we get $i_{rms}^2 = 3 	imes i^2$.Given $i = 2 \ A$,we have $i_{rms}^2 = 3 	imes (2)^2 = 3 	imes 4 = 12$.Therefore,$i_{rms} = \sqrt{12} = 2\sqrt{3} \approx 3.46 \ A$.

What is the $r.m.s.$ value of an alternating current which,when passed through a resistor,produces heat that is thrice the heat produced by a direct current of $2 \ A$ in the same resistor (in $A$)?

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