Question

7) An AC generator has the following emf: ε-6, sin[or-(π /4)], where ε,-30V and ω-350 rad/s. The current produced in a conne

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Answer #1

a)

From

\varepsilon =\varepsilon _{m}Sin\left [ \omega t-\frac{\pi }{4} \right ]

at E=Em

\varepsilon _{m} =\varepsilon _{m}Sin\left [ \omega t-\frac{\pi }{4} \right ]

Sin\left [ \omega t-\frac{\pi }{4} \right ]=1

\omega t - \frac{\pi }{4} =Sin^{-1}\left ( 1 \right ) = \frac{\pi }{2}

Given W=350 rad/s

350t= \frac{\pi }{2} + \frac{\pi }{4} = 2.3562

t = 2.3562/350

t=6.732*10-3 s or 6.732 ms

b)

I(t) = I_{m}Sin\left ( \omega t - \frac{3\pi }{4} \right )

=>I_{m} = I_{m}Sin\left ( \omega t - \frac{3\pi }{4} \right )

Sin\left ( \omega t - \frac{3\pi }{4} \right ) = 1

\omega t - \frac{3\pi }{4} = Sin^{-1}(1) = \frac{\pi }{2}

350 t = \frac{\pi }{2} +\frac{3\pi }{4} = 3.927

t=3.927/350

t=0.01122 s or 11.22 ms

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