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

5 answers

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?
yes it can because 0.004 is less than 0.01???
yes
ok, the back of the book is wrong then because the answer says: "no" ...
and then i got confused, k thank you!
go through my arithmetic slowly, this old brain tends to make mistakes lately.

make sure your calculator is set to radians