Alternating Current Part 1

Given, equation of alternating current,
i=[√42‌sin(

2π

T

t)+10]A
From given equation, we get
i=i1+i2
where, i1=√42‌sin(

2π

T

t)‌A and i2=10A
Now, i1 is oscillating current, whereas i2 is direct current and its value does not change with time.
(i1)rms=

√42

√2

=√21A
(i2)rms=10A
We know that, irms2=(i1)rms2+(i2)rms2
Substituting the values, we get
irms=√(√21)2+102=√121
⇒irms=11A
Thus, RMS value of given equation of current is 11 A.