Question

An ac generator operates at a rotational frequency of 60 Hz and produces a maximum emf of 100 V. Assume that its output at is zero. What is the instantaneous emf (a) at ? (b) at ? (c) at t? (d) How much time elapses between successive 0-volt outputs? (e) What maximum emf would this generator produce if it were operated, instead, at 120 Hz?

Answer 1

(a). The instantaneous emf at
`t = (1)/(240)` is 100 V.

(b). The instantaneous emf at
`t = (1)/(120)` is 0 V.

(c). The instantaneous emf at
`t = (t)/(376.9)` is
`100*\sin(57.29\ t)`.

(d). The time elapses is 0.00416 sec.

(e). The maximum voltage is 100 V.

Step-by-step explanation:

Given that,

Frequency = 60 Hz

Emf = 100 V

We need to calculate the angular frequency

Using formula of angular frequency

`\omega=2\pi f`

Put the value into the formula

`\omega=2\pi*60`

`\omega=376.9\ rad/s`

(a). At
`t = (1)/(240)`

We need to calculate the instantaneous emf

Using formula of instantaneous emf

`V_(inst)=V\sin\omega t`

Put the value into the formula

`V_(inst)=100\sin*376.9(1)/(240)`

`V_(inst)=100\sin(360*(1.57)/(2\pi))`

`V_(inst)=100*\sin90`

`V_(inst)=100\ V`

(b). At
`t =(1)/(120)`

We need to calculate the instantaneous emf

Using formula of instantaneous emf

`V_(inst)=V\sin\omega t`

Put the value into the formula

`V_(inst)=100\sin*376.9(1)/(120)`

`V_(inst)=100\sin(360*(3.14)/(2\pi))`

`V_(inst)=100*\sin180`

`V_(inst)=0\ V`

(c). At
`t = (t)/(376.9)`

We need to calculate the instantaneous emf

Using formula of instantaneous emf

`V_(inst)=V\sin\omega t`

Put the value into the formula

`V_(inst)=100\sin*376.9* (t)/(376.9)`

`V_(inst)=100\sin(360*( t)/(2\pi))`

`V_(inst)=100*\sin(57.29\ t)`

(d). The maximum instantaneous voltage occurred at
`t =(1)/(240)` is 100 V and the maximum instantaneous voltage occurred at
`t =(1)/(120)` is 0 V .

We need to calculate the time elapses

Using formula of time

`t=(1)/(120)-(1)/(240)`

Put the value into the formula

`t=(1)/(240)`

`t=0.00416\ sec`

(e). The maximum voltage does not depend upon the frequency.

So, The maximum voltage is 100 V.

Hence, (a). The instantaneous emf at
`t = (1)/(240)` is 100 V.

(b). The instantaneous emf at
`t = (1)/(120)` is 0 V.

(c). The instantaneous emf at
`t = (t)/(376.9)` is
`100*\sin(57.29\ t)`.

(d). The time elapses is 0.00416 sec.

(e). The maximum voltage is 100 V.