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Question

Average heat produced per unit time during a cycle of AC is the same as produced by DC with current i=

A
iavg
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B
irms
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C
i2avg
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D
ipeak
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Solution

The correct option is B irms
For AC, i=i0sinωt

Therefore, the instantaneous value of heat produced in time dt across a resistance R is

dH=i2Rdt=i20Rsin2ωt dt

Average value of heat produced per unit of time during a cycle of AC,

Havg=T0dHT0dt

=2πω0(i20Rsin2ωt)dt2πω0dt

=i20R2πω0(sin2ωt)dt2πω0dt

⎢ ⎢ ⎢ ⎢ ⎢2πω0(sin2ωt)dt=12×2πω⎥ ⎥ ⎥ ⎥ ⎥


=i202R=i2rmsR

Heat produced per unit time when a DC current i flows through a resistance R is,

H=i2R

On comparing the heat produced during a cycle of AC and DC we get,

i=irms

Hence, option (B) is correct.

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