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Can you please tell me the derivation of rms value of current.

Can you please tell me the derivation of rms value of current.


 

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1 Answers

Nirmal Singh.
askIITians Faculty 44 Points
10 years ago
An alternating current is given by i = i0 sin(wt+phie)
The instantaneous current i could be positive or negative at a guiven instant but quantity i2 always remains positive and hence its average is also positive. The average of i2 over a time period is
i2(bar) = integration from 0 to T of (i2 dt) / integration from 0 to Tof (dt)
on putting value of i = i0 sin(wt+phie)
= 1/T[ integration from 0 to T of i02 sin2 (wt+phie)]dt
= i02/2T integration from 0 to T of [ {1-cos2(wt+phie)}]dt
= i02/2T[t - sin2(wt+phie)/ 2w] from o to T
= i02/2T [T - sin(4pie+2phie) - sin 2pie/ 2w] = i0 2 / 2
This is Know as the mean square current .The square root mean square current or rms.current.thus irms = square root (i2 bar) = i0 / squareroot(2)
Thanks & Regards,
Nirmal Singh,
askIITians Faculty.

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