Question

The voltage, V, in volts, applied to an electric circuit can be modeled by the equation

V= 167sin (120 pi x)

where x is the time, in seconds. A component in the circuit can safely withstand a voltage of more than 120 V for 0.01 s or less.

Determine the length of time the voltage is greater than 120 V on each half-cycle.

Answer 1

set the voltage equal to 120
120 = 167sin(120pix)
.7185628 = sin(120pix)
so 120pix = .8017336 or 120pix = pi - .8017336

x = .8017336/(120pi) or x = (pi - .8017336)/(120pi)
x = .00213 or x = .00621

so it will be greater than 120 for the time period between the times of .00213 seconds and .00621 seconds

that span of time is .00621-.00213 seconds or .0041 seconds

Therefore the component is safe.