R.M.S value of current

$I=3+4\sin \left(\omega t+\frac{\pi }{3}\right)$ is:

We must employ the idea of RMS current, which is a statistical measure of the size of a current varying from different values, in order to get the Root Mean Square value of the current. For sinusoidal systems, the peak current and voltage are multiplied by the square root of two to get the RMS current and voltage.

Given that the current value is
$i=3+4\sin \left(\omega t+\frac{\pi }{3}\right)$
After squaring the amount, we must get the mean value of the functions in order to determine the RMS value of current.
By squaring the two sides, we obtain
$i^2={\left[3+4\sin \left(\omega t+\frac{\pi }{3}\right)\right]}^2$
$\Rightarrow i^2=9+16{\sin }^2\left(\omega t+\frac{\pi }{3}\right)+24\sin \left(\omega t+\frac{\pi }{3}\right)$
Using the current's mean value as a starting point
$i^2=9+16\left(\frac{1}{2}\right)+24\left(0\right)$
Here, ${\sin }^{2}x=\frac{1}{2}\& \sin x=0$

$\Rightarrow i^2=17$
$\therefore \sqrt{i^2}=\sqrt{17}A$
The current's RMS value is stated as$\sqrt{17}A$.

Hence, the correct answer is option B.