Final answer:
The r.m.s value of the given AC is 10 amperes, and it takes 0.005 seconds (5 milliseconds) for the current to reach its maximum value from zero.
Step-by-step explanation:
The r.m.s. value of an alternating current (AC) is 0.707 times the peak value.
Given that the peak current (I0) is 14.14 amperes, the r.m.s. value (Irms) can be calculated by multiplying the peak current by 0.707.
Irms = I0 × 0.707
= 14.14 A × 0.707
= 10 amperes (approx.)
To find the time it takes for the current to reach its maximum value from zero, we consider that for a sinusoidal waveform, the time (t) to reach the peak from zero corresponds to a quarter of the period (T) of the waveform.
The frequency (f) is given as 50 Hz, which means the period T is the inverse of the frequency.
T = 1/f = 1/50
= 0.02 seconds (or 20 milliseconds)
Therefore, the time to reach the peak value from zero is a quarter of the period, which is
T/4 = 0.02 s / 4
= 0.005 seconds (or 5 milliseconds).