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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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 $A$)?

Similar Questions

An $AC$ source rated $220\, V, 50\, Hz$ is connected to a resistor. The time taken by the current to change from its maximum value to the $rms$ value is:

If $I_1, I_2, I_3$ and $I_4$ are the respective $r.m.s.$ values of the time-varying currents as shown in the four cases $I, II, III$ and $IV$,then identify the correct relation.

The instantaneous value of current in an $A.C.$ circuit is $I = 3 \sin \left(50 \pi t + \frac{\pi}{4}\right) \text{ A}$. The current will be maximum for the first time at

$A$ resistance of $40 \,\Omega$ is connected to a source of alternating current rated $220 \,V, 50 \,Hz$. Find the time taken by the current to change from its maximum value to its $rms$ value.

The $r.m.s.$ voltage of the waveform shown is......$V$

Vedclass Test Series

Exam Paper Generator

Online Exam Module