Question

The AC voltage coming out of a standard wall plug in the United States can be expressed as the function V(t) = 120sin(120*pi*t), where t represents time (in seconds) and V is the voltage. We will let t be greater than or equal to 0 for simplicity.

A. Make an accurate sketch of V(t).
B. What is the maximum value of V?
C. What is the minimum value of V?
D. What are the first three times that V=0?
E. What are the first two times that V=60?
F. What are the first two times that V=10? You may round your answer to 1 significant digit.

Answer 1

V(t) = 120sin(120*pi*t)
V(t) = 120sin(377t)
377*t = The angle in radians.

B. Vmax=120sin(377*1/240)=120sin(90o)= 120 Volts.

C. Vmin=120sin(377*1/80)=120sin(270o)= -120 Volts.

D. 0, 1/120, and 1/60 Seconds.

E. 120sinA = 60
sinA = 60/120 = 0.5
A = 30o.
t=(30o/360o) * 1/60 = 1/360=0.00278 s.

A = 180-Ar = 180-30 = 150o
t = (150o/360o) * 1/60 = 0.00694 s.

F. 120sinA = 10
sinA = 0.08333
A = 4.78o
t =
t = (4.78/360) * 1/60 = 0.00022 s.

A = 180-4.78 = 175.22o
t = (175.22/360) * 1/60 = 0.0081 s.


NOTES

2pi*F = 377 Radians/s.
F = 377/2pi = 377/6.28 = 60 Hz
P = 1/60 Seconds. = The period.