Question

Write an expression for the instantaneous voltage ????(????) delivered by an ac generator supplying 120 V rms at 60 Hz. Assume the voltage is 0 at time ????=0, and leave the factors in exact form; do not round their values. Write the argument of the sinusoidal function to have units of radians, but omit the units.

Answer 1

`V = 120 \sqrt {2} sin (120 \pi t)`

Step-by-step explanation:

We start from the ideal conditions previously given, as well

`V_ {rms} = 120V`

`f = 60Hz`

We understand that the formula for Maximum Voltage is given by,

`V_ {max} = \sqrt {2} V_ {rms}`

In turn, we can take the expression given for the Instantaneous Voltage, which is defined as,

`V = \sqrt {2} V_ {rms} sin (2 \pi f t)`

Replacing all expressions in one,

`V = 120 \sqrt {2} Vsin (2 \pi (60Hz) t)`

`V = 120 \sqrt {2} V sin ((120 \pi rad / s) t)`

Eliminating units for better reading

`V = 120 \sqrt {2} sin (120 \pi t)`