Question

the voltage, v, in volts, applied to an electric circuit can be modelled by the equation v=167sin(120pi)(t), where t is the time, in seconds. A component in the circuit can safely withstand a voltage of more than 120 V for 0.01 sec or less.
a) determine the length of the time that the voltage is greater than 120 V on each half-cycle.
b)is it safe to use this component in this circuit? justify your answer.

can you please explain to me clearly how I to do this q

Answer 1

since your amplitude is 167, that becomes your maximum voltage

let's solve when the voltage is 120

120 = 167sin(120pi)t
.71856 = sin(120(pi)t)

so 120pi(t) = .80173 (in first quadrant)
or 120pi(t) = pi - .80172 = 2.3399 (2nd quadrant)
in I:
t = .80173/(120pi) = .00212 seconds
in II:
t = .00621

so the voltage is above 120 volts from
a time of .00621-.00212 or .00441 seconds

so what do you think?

Answer 2

yes it can because 0.004 is less than 0.01???

Answer 3

yes

Answer 4

ok, the back of the book is wrong then because the answer says: "no" ...
and then i got confused, k thank you!

Answer 5

go through my arithmetic slowly, this old brain tends to make mistakes lately.

make sure your calculator is set to radians