Question

The electromotive force V of an alternating current circuit at time t can be describe by the

following function, where V is volts and t is in seconds. V(t) = 220sin(180πt). How many cycles
will the circuit run through in 1 minute?​

Answer 1

5400 cycles

Explanation:

You have the following function:

`V(t)=220sin(180\pi t)`

where t is in seconds.

In order to find the number of cycles in 1 minute, you first calculate the frequency of the function, which is given by:

`f=(180\pi)/(2\pi)=90s^(-1)`

The number of cycles is then given by:

`n=ft=(90s^(-1))(60s)=5400\ cycles`

There are 5400 cycles in 1 minute