Question

The output voltage of an AC generator is of the form V = V​0 sin(2πft). A typical frequency in household circuits is 60 Hz. Using radians for angular measure in this equation, what is the factor 2πf in radians per second for this frequency?

Answer 1

Value of factor 2πf in radians per second for this frequency is 377 rad/s.

Step-by-step explanation:

Given :

Equation of output voltage ,
`V=V_o\ sin( 2\pi ft)`

Frequency , f = 60 Hz .

We know , frequency is converted to angular frequency with units rad /s as :

`\omega=2\pi f`

Putting value of f in above equation .

We get :

`\omega=2* \pi * 60\\\omega = 376.99\ rad/s\\or\ , \omega=377 \ rad/s`

So , value of factor 2πf in radians per second for this frequency is 377 rad/s.