CBSE Class 12 · 2007 · Alternating CurrentShort Answer

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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?

Answer: $I_{a v} = \frac{2}{π} I_{0} = 0.637 I_{0}$ , $I_{r m s} = \frac{I _{0}}{2} = 0.707 I_{0}$ ; here $I_{a v} = 3.18$ A and $I_{r m s} = 3.54$ A.

Solution

The average value (over a half cycle) is the steady current that transfers the same charge in the same time as the a.c. does in a half cycle; the rms value is the steady current that produces the same heating in a resistor in the same time.

I_{a v} = \frac{2}{π} I_{0} = 0.637 I_{0}, I_{r m s} = \frac{I _{0}}{2} = 0.707 I_{0}

Here

I_{0} = 5

A, so

I_{a v} = 0.637 \times 5 = 3.18 A, I_{r m s} = 0.707 \times 5 = 3.54 A

CBSE Class 12 Board · 2007 · Subjective

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CBSE Class 12 · 2007 · Alternating CurrentShort Answer

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