A

The root mean square (rms) value for an alternating current is defined as \( I_{rms} = \frac{I_0}{\sqrt{2}} \), where \( I_0 \) is the peak current.\
For a sinusoidal waveform, the current can be represented as \( I(t) = I_0 \sin(\omega t) \), where \( \omega = 2\pi f \) and \( f \) is the frequency.
Given that the frequency (f) is 50 Hz, we find:
\( \omega = 2\pi \times 50 = 100\pi \) rad/s.
The rms value is reached at a phase of \( \frac{\pi}{2} \) radians. The time corresponding to this phase is:
\( t = \frac{\frac{\pi}{2}}{\omega} = \frac{\frac{\pi}{2}}{100\pi} = \frac{1}{200} \) seconds.
Therefore, the time required for the current to change its value from zero to the rms value is \( 0.005 \) seconds or 5 milliseconds.