Respuesta :
Answer:
(a). The instantaneous emf at [tex]t = \dfrac{1}{240}[/tex] is 100 V.
(b). The instantaneous emf at [tex]t = \dfrac{1}{120}[/tex] is 0 V.
(c). The instantaneous emf at [tex]t = \dfrac{t}{376.9}[/tex] is [tex]100\times\sin(57.29\ t)[/tex].
(d). The time elapses is 0.00416 sec.
(e). The maximum voltage is 100 V.
Explanation:
Given that,
Frequency = 60 Hz
Emf = 100 V
We need to calculate the angular frequency
Using formula of angular frequency
[tex]\omega=2\pi f[/tex]
Put the value into the formula
[tex]\omega=2\pi\times60[/tex]
[tex]\omega=376.9\ rad/s[/tex]
(a). At [tex]t = \dfrac{1}{240}[/tex]
We need to calculate the instantaneous emf
Using formula of instantaneous emf
[tex]V_{inst}=V\sin\omega t[/tex]
Put the value into the formula
[tex]V_{inst}=100\sin\times376.9\dfrac{1}{240}[/tex]
[tex]V_{inst}=100\sin(360\times\dfrac{1.57}{2\pi})[/tex]
[tex]V_{inst}=100\times\sin90[/tex]
[tex]V_{inst}=100\ V[/tex]
(b). At [tex]t =\dfrac{1}{120}[/tex]
We need to calculate the instantaneous emf
Using formula of instantaneous emf
[tex]V_{inst}=V\sin\omega t[/tex]
Put the value into the formula
[tex]V_{inst}=100\sin\times376.9\dfrac{1}{120}[/tex]
[tex]V_{inst}=100\sin(360\times\dfrac{3.14}{2\pi})[/tex]
[tex]V_{inst}=100\times\sin180[/tex]
[tex]V_{inst}=0\ V[/tex]
(c). At [tex]t = \dfrac{t}{376.9}[/tex]
We need to calculate the instantaneous emf
Using formula of instantaneous emf
[tex]V_{inst}=V\sin\omega t[/tex]
Put the value into the formula
[tex]V_{inst}=100\sin\times376.9\times \dfrac{t}{376.9}[/tex]
[tex]V_{inst}=100\sin(360\times\dfrac{ t}{2\pi})[/tex]
[tex]V_{inst}=100\times\sin(57.29\ t)[/tex]
(d). The maximum instantaneous voltage occurred at [tex]t =\dfrac{1}{240}[/tex] is 100 V and the maximum instantaneous voltage occurred at [tex]t =\dfrac{1}{120}[/tex] is 0 V .
We need to calculate the time elapses
Using formula of time
[tex]t=\dfrac{1}{120}-\dfrac{1}{240}[/tex]
Put the value into the formula
[tex]t=\dfrac{1}{240}[/tex]
[tex]t=0.00416\ sec[/tex]
(e). The maximum voltage does not depend upon the frequency.
So, The maximum voltage is 100 V.
Hence, (a). The instantaneous emf at [tex]t = \dfrac{1}{240}[/tex] is 100 V.
(b). The instantaneous emf at [tex]t = \dfrac{1}{120}[/tex] is 0 V.
(c). The instantaneous emf at [tex]t = \dfrac{t}{376.9}[/tex] is [tex]100\times\sin(57.29\ t)[/tex].
(d). The time elapses is 0.00416 sec.
(e). The maximum voltage is 100 V.
