The current I an electrical circuit at time t measured in se

The current I, an electrical circuit at time t, measured in seconds, is shown below.

a. Find the amplitude and the period.

b. How many cycles are in one second?

Solution

l=270sin(30pit)

comaparing it with y = Asin(Bt)

a). Amplitude (A) = 270

period = 2pi/B

so B = 30pi

period = 2pi/30pi

= 1/15

b).

frequency = 2pi/period

frequency = 2pi/1/15

frequency = 30pi

By reciprocal relation of period and frequency:
T = 1/f

T = 1/30pi


T = 0.0106 seconds



Given time interval:
t = 1 sec

Number of complete cycles fitting in to this time interval:
N = t/T
N= 1/0.0106
Result:
N = 94 Cycles