An alternating current represented by the equation i= 4,5 sin (100×pie×t) flows through a certain series circuit. The time period is 0,02 seconds. It takes t = 1 / (200) seconds for the current to reach its maximum. Calculate the magnitude of the instantaneous current 1ms after the begging of a cycle.
To find the magnitude of the instantaneous current 1ms after the beginning of a cycle, you need to substitute the value of t in the equation i= 4.5 sin (100*pi*t).
Given:
Time period, T = 0.02 seconds
t = 1/200 seconds
From the equation, we know that one cycle of the current waveform is completed in one time period.
Since T = 0.02 seconds, there are 0.02 seconds in one full cycle.
Therefore, the number of cycles in 1ms (0.001 seconds) is:
Number of cycles = (0.001 seconds) / (0.02 seconds) = 0.05 cycles
To find the magnitude of the instantaneous current 1ms after the beginning of a cycle, we need to find the value of sin(100*pi*t) when t = 1/200 seconds.
Substitute t = 1/200 seconds in the equation:
i = 4.5 * sin (100*pi*t)
= 4.5 * sin (100*pi * 1/200)
= 4.5 * sin (pi/2)
= 4.5 * 1
= 4.5 Amperes
Therefore, the magnitude of the instantaneous current 1ms after the beginning of a cycle is 4.5 Amperes.