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

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 i_rms = square root (i² bar) = i₀ / squareroot(2)
Thanks & Regards,

Nirmal Singh,

askIITians Faculty.