The study of alternating electric current requires the solutions of equations of the form i equals Upper I Subscript max Baseline sine 2 pi ft comma for time t in seconds, where i is instantaneous current in amperes, Imax is maximum current in amperes and f is the number of cycles per second. Find the least positive value of t, given the following data. i=180, Imax=200, f=50

Question

Physics

Paddington

9 March, 10:45

The study of alternating electric current requires the solutions of equations of the form i equals Upper I Subscript max Baseline sine 2 pi ft comma for time t in seconds, where i is instantaneous current in amperes, Imax is maximum current in amperes and f is the number of cycles per second. Find the least positive value of t, given the following data. i=180, Imax=200, f=50

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Madalyn Mcmahon · Answer 1

i = Imax sin2πft

given i = 180, Imax = 200, f = 50, t = ?

Put the give values in the equation above

180 = 200 sin 2πft

sin 2πft =.9

sin2π x 50t =.9

sin 360 x 50 t = sin (360n + 64)

360 x 50 t = 360n + 64

360 x 50 t = 64, (putting n = 0 for least value of t)

18000 t = 64

t = 3.55 ms.