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 = 0,286 seconds for the current to reach its maximum. The magnitude of instantaneous current after 1 ms is 2,154 A. Calculate the time it takes current to reach 3,75A
To calculate the time it takes for the current to reach 3.75A, we can use the equation for the instantaneous current:
i = 4.5 sin (100πt)
Given that the magnitude of the instantaneous current after 1ms is 2.154A, we can substitute this value into the equation:
2.154 = 4.5 sin (100π * (1/1000))
Simplifying the equation:
2.154 = 4.5 sin (π/500)
Using a calculator to find the inverse sine of 2.154/4.5:
0.491 = π/500
Multiplying both sides by 500 and dividing by π:
0.491 * 500 / π = t
t ≈ 7.82ms
Therefore, it takes approximately 7.82ms for the current to reach 3.75A.