If an a.c is represented by I = IoSinωt. Calculate the instantaneous value

Question

IF AN A•C IS REPRESENTED BY I = IoSinωt. CALCULATE THE INSTANTANEOUS VALUE OF SUCH A CURRENT, IF IN A CIRCUIT IT HAS A RMS VALUE OF 15•OA WHEN ITS PHASE ANGLE IS 30°
(WAEC 1989)

Solution

Data:

The root mean square value of the current, I_r.m.s = 15.0 A, The phase angle, θ = ωt = 30^o, peak current I_o= ?

Formula:

I_o= I_r.m.s x √2,

Instantaneous current I = I_oSinωt

Solving the problem:

Using the first formula and by applying our data: I_o= I_r.m.s x √2 = 15 x √2 = 21.21 A

Using the second formula: I = I_oSinωt = 21.21 Sin30^o

I = 21.21 x 0.5 = 10.61 A.