(A) The heat produced by a heater in a resistance $R$ over time $t$ is given by $H = \frac{V^2}{R} t$.For $d.c.$ voltage,$H_{dc} = \frac{V_{dc}^2}{R}

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(A) The heat produced by a heater in a resistance $R$ over time $t$ is given by $H = \frac{V^2}{R} t$.For $d.c.$ voltage,$H_{dc} = \frac{V_{dc}^2}{R} t$.For $a.c.$ voltage,the heat produced is determined by the $r.m.s.$ value of the voltage,$H_{ac} = \frac{V_{rms}^2}{R} t$.Given that the heat produced is the same in both cases $(H_{ac} = H_{dc})$,we have:$\frac{V_{rms}^2}{R} t = \frac{V_{dc}^2}{R} t$$V_{rms}^2 = V_{dc}^2$$V_{rms} = V_{dc}$Given $V_{dc} = 110 \, V$,therefore $V_{rms} = 110 \, V$.

Class 12 Physics Alternating Current Alternating Current, Voltage (rms and Average)

Easy

$A$ $110 \, V$ $d.c.$ heater is used on an $a.c.$ source,such that the heat produced is the same as it produces when connected to $110 \, V$ $d.c.$ in the same time intervals. What would be the $r.m.s.$ value of the alternating voltage?

A
$110$
B
$220$
C
$330$
D
$440$

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Alternating Current

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Alternating Current, Voltage (rms and Average)

Find the time required for $50\,Hz$ alternating current to change its value from zero to maximum value.

Medium

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$A$ group of lamps having a total power rating of $1000 \,W$ is supplied by an $AC$ voltage of $E = 200 \sin(310t + 60^{\circ})$. The $r.m.s.$ value of the current flowing through the circuit is:

MediumMHT CET 2023

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The $r.m.s.$ value of an $AC$ of $50 \ Hz$ is $10 \ A$. The time taken by the alternating current in reaching from zero to maximum value and the peak value of current will be:

Medium

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The frequency of an alternating voltage is $50 \ Hz$. The time taken for the instantaneous voltage to increase from zero to half of its peak voltage is:

MediumTS EAMCET 2025

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$A$ resistance of $20 \Omega$ is connected to a source of an alternating potential $V = 200 \sin (10 \pi t)$. If $t$ is the time taken by the current to change from the peak value to rms value,then $t$ is (in seconds).

MediumAP EAMCET 2024

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$A$ $110 \, V$ $d.c.$ heater is used on an $a.c.$ source,such that the heat produced is the same as it produces when connected to $110 \, V$ $d.c.$ in the same time intervals. What would be the $r.m.s.$ value of the alternating voltage?

Similar Questions

Find the time required for $50\,Hz$ alternating current to change its value from zero to maximum value.

$A$ group of lamps having a total power rating of $1000 \,W$ is supplied by an $AC$ voltage of $E = 200 \sin(310t + 60^{\circ})$. The $r.m.s.$ value of the current flowing through the circuit is:

The $r.m.s.$ value of an $AC$ of $50 \ Hz$ is $10 \ A$. The time taken by the alternating current in reaching from zero to maximum value and the peak value of current will be:

The frequency of an alternating voltage is $50 \ Hz$. The time taken for the instantaneous voltage to increase from zero to half of its peak voltage is:

$A$ resistance of $20 \Omega$ is connected to a source of an alternating potential $V = 200 \sin (10 \pi t)$. If $t$ is the time taken by the current to change from the peak value to rms value,then $t$ is (in seconds).

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