Question

Before electrical specifications were standardized, many different frequencies were used to deliver power to homes. For example, a power plant might have delivered electricity at a frequency of 35 cycles per second. If the current in amps (i) of this electricity and time (t) are related sinusoidally, and the current is at its maximum of 8 at t = 0, what is the current at t = 1? Give an exact answer.

Answer 1

1 is 4.11090100841081.

Answer 2

Explanation:

1. First, recall that the relationship between the current (i) and time (t) is sinusoidal. This means the current is in the form of a sine wave.

2. Recall that the maximum current is 8 at t = 0. Thus, the maximum is 8 and the minimum is 0.

3. Using trigonometric identities, we can calculate the current at t = 1. We know that at t = 0, the current is 8, and at t = 1, the current is i. We can calculate i by using the equation for a sine wave:

i = 8sin(35 * PI * t).

4. Substituting t = 1 into the equation, we get:

i = 8sin(35 * PI *1)

5. Solving the equation gives us i = 8sin(35PI).

6. Using a calculator, we can calculate that the current at t = 1 is 4.11090100841081.

Therefore, the current at t = 1 is 4.11090100841081.