Question

4. The usual 110-V household alternating current varies from -155 V

to 155 V with a frequency of 60 cycles/ sec (frequency is the
reciprocal of period). Assume the current starts at rest and then
rises.

Make a sketch of the curve.

Write an equation to describe the curve:_

Determine the value of y when t = 1/90 sec.:_

Approximate the value of t when y = 100 for the first time:_

Answer 1

The equation for the alternating current can be described by: y = 155 sin(120πt)

Where y is the voltage in volts (V) and t is the time in seconds (s).

To find the value of y when t = 1/90 s:

y = 155 sin(120π(1/90))

y ≈ 30.8 V

To approximate the value of t when y = 100 V for the first time, we need to solve the equation for t:

100 = 155 sin(120πt)

sin(120πt) = 100/155

t = arcsin(100/155)/(120π)

t ≈ 0.001 s

Therefore, the value of t when y = 100 V for the first time is approximately 0.001 seconds