Question

common household electric current is called alternating current because the current alternates direction within the wires. the voltage v in a typical 115 - volt outlet can be expressed by the function v(t)=163 sin ωt, where ω is the angular speed (in radians per second) of the rotating generator at the electrical plant and t is the time measured in seconds. it is essential for electric generators to rotate at precisely 60 cycles per sec. complete parts (a) and (b).
(a) how many times does the current oscillate in 0.25 sec?

Explanation:

Step1: Analyze the given information

We know that the generator rotates at 60 cycles per second.

Step2: Calculate the number of oscillations in 0.25 seconds

Use the formula \(N = f\times t\), where \(f = 60\) cycles per second (frequency) and \(t=0.25\) seconds (time).
Substitute the values into the formula: \(N = 60\times0.25\).

$$N=\frac{60}{1}\times\frac{25}{100}=\frac{60\times25}{100}=\frac{1500}{100} = 15$$

Answer:

15