A steady current of magnitude $I$ and an $A C$ current of peak value $I$ are allowed to pass through identical resistor for the same time. The ratio of heat produced in the two resistors will be :

2 : 1

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1 : 2

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1 : 1

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None of these

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Solution

The correct option is C $2 : 1$
$H_{D C} = I^{2} R t$
$H_{A C} = I_{r m s}^{2} R t = {(\frac{I}{\sqrt{2}})}^{2} R t = \frac{I^{2} R t}{2}$
$∴ \frac{H_{D C}}{H_{A C}} = \frac{2}{1}$

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Similar questions

Q. The runs value of

A C

which when passed through a resistor produced heat, which is twice that produced by a steady current of

1.414 A

in the same resistor is:

The heat produced by passing an electric current through a fixed resistor is proportional to the square of :
(a) magnitude of resistance of the resistor
(b) temperature of the resistor
(c) magnitude of current
(d) time for which current is passed

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A steady current of magnitude I and an AC current of peak value I are allowed to pass through identical resistor for the same time. The ratio of heat produced in the two resistors will be :

The correct option is C 2:1HDC=I2RtHAC=I2rmsRt=(I√2)2Rt=I2Rt2∴HDCHAC=21

A steady current of magnitude $I$ and an $A C$ current of peak value $I$ are allowed to pass through identical resistor for the same time. The ratio of heat produced in the two resistors will be :

The correct option is C $2 : 1$
$H_{D C} = I^{2} R t$
$H_{A C} = I_{r m s}^{2} R t = {(\frac{I}{\sqrt{2}})}^{2} R t = \frac{I^{2} R t}{2}$
$∴ \frac{H_{D C}}{H_{A C}} = \frac{2}{1}$