To find the r.m.s value of an alternating current mathematically, we need to have:

Explanation

The Root Mean Square (R.M.S) value of an alternating current is calculated using the following formula:[ I_{{rms}} = sqrt{frac{1}{T} int_{0}^{T} i^2(t) ,dt} ]where ( i(t) ) is the instantaneous current at time ( t ) in one cycle, and ( T ) is the time period of one cycle.The R.M.S value is obtained by taking the square root of the mean value of the square of the instantaneous current over one complete cycle.- (a) Mean value of 12: This is not correct. The R.M.S value is related to the mean value of the square of the instantaneous current.- (b) Square root of mean value of 12: Correct. The R.M.S value is obtained by taking the square root of the mean value of the square of the instantaneous current.- (c) Square root of 12: This is not correct. The correct expression involves the mean value of the square of the instantaneous current.- (d) Square of 1/2: This is not correct. The R.M.S value is not related to the square of 1/2.So, the correct answer is (b) Square root of mean value of 12.