Question

1. An alternating current is given by the formula

I = 30 sin (50 t + 0.26) amps

a) Find the amplitude, periodic time, frequency, and phase angle

b) Find the value of the current at 18ms

c) Find the time at which the current first reaches 20 amps 

d) Plot the curve between 0 and 20ms

Answer 1

Amplitude = 30

frequency

    $50=\omega=2\Pi f$

$f=50/2\Pi=7.957747155 Hz$

periodic time

$T=1/f=1/7.957747155=0.125663706 seconds$

$=125.663706ms$

phase angle

$=0.26radians$

$=0.26*180^{\circ} /\pi)=14.8969 \, degrees$

at 18 ms $I=30sin(50(0.018)+0.26)=27.504$

$20=30sin(50t +0.26)$

$2/3=sin (50t+0.26)$

$41.8103149=50t+0.26$

$t=0.831006297 seconds$

graph