19 The voltage of an electric current is given by E Eo sin 2

19. The voltage of an electric current is given by E Eo sin 2mft, where f is the frequency, Eo is the maximum voltage, and t is in seconds a. Solve for t. b. Find the smallest positive t value if Eo = 12, E = 5, and f = 100.

Solution

the voltage of an electric current is given by

E = Eo*sin(2pi*f*t)

(a) arcsin(E/Eo) = 2pi*f*t

t = [arcsin(E/Eo)]/(2pi*f)

(b) Eo = 12

E = 5

f = 100

Then

t = [arcsin(E/Eo)]/(2pi*f) = [arcsin(5/12)]/(2pi*100)

t = 0.43/628.3 = 6.84*10^-4 s