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Alternating Current — Physics STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 SciencePhysicsAlternating Current2 Marks
Question
Distinguish between the terms 'average value' and 'rms value' of an alternating current. The instantaneous current from an a.c. source is I = 5 sin (314 t) ampere.
What are the average and rms values of the current?
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Answer

Average value of an alternating current over time T is
$\text{I}_{\text{AV}} = \frac{1}{\text{T}}\int\limits_{0}^{T}\text{I}(\text{t})\text{dt}$
rms value of an alternating current is that value of stready current which when flowing through a resistance for a certain amount of time produces same amount of heat as the given A.C. does in the same resistance in the same time.
Average value over half cycle is ${2\over\pi}\text{I}_{0} = 3.18\text{A}$
or Aveage value over complete cycle is zero
rms value is ${\text{I}_{0}\over\sqrt{2}} = 3.54\text{A}\text{ or }{5\over\sqrt{2}}\text{A}.$

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