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Question
State the rms value of an alternating current? Write the relation between the rms value and peak value of an alternating current that varies with time.
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Solution
- The constant current which produces the same amount of heat in a given resistance in a given time as is produced by an alternating current, when flowing through the same resistance for the same time is called the root mean square (rms) value of current.
It is given by, irms = `"I"_0/sqrt2 = 0.707 "i"_0`. - The relation between the rms value and peak value of alternating current is given by,
`"i"_"rms"^2 = (int_0^(2pi) "i"^2 "d"theta)/(2pi) = 1/(2pi)int_0^(2pi) "i"_0^2 sin^2 theta "d"theta`
= `"i"_0^2/(2pi) int_0^(2pi) ((1 - cos 2theta))/2 "d"theta` ...............(∵ cos 2θ = 1 - sin2θ)
= `"i"_0^2/(2 xx 2pi)[(theta - (sin 2theta)/2)]_0^(2pi)`
= `"i"_0^2/2`
∴ irms = `"i"_0/sqrt2 = 0.707 "i"_0`
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