Question 398: AC fundamentals

Question

An alternating e.m.f. is $$\mathrm{e}=\mathrm{e}_0 \sin \omega \mathrm{t}$$. In what time the e.m.f. will have half its maximum value, if '$$\mathrm{e}$$' starts from zero? ($$\mathrm{T}=$$ time period, $$\sin 30^{\circ}=0.5$$)

Accepted Answer

$$\mathrm{e}=\mathrm{e}_0 \sin \omega \mathrm{t}$$
If $$\mathrm{e}=\frac{e_0}{2}$$ then $$\frac{e_0}{2}=e_0 \sin \omega t$$
$$	herefore \sin \omega \mathrm{t}=\frac{1}{2} \quad 	herefore \quad \omega \mathrm{t}=30^{\circ}=\frac{\pi}{6} \mathrm{rad}$$
$$	herefore \frac{2 \pi}{T} \cdot t=\frac{\pi}{6} \quad 	herefore \quad \mathrm{t}=\frac{\mathrm{T}}{12}$$

Answer

$$\frac{\mathrm{T}}{12}$$

Answer

$$\mathrm{\frac{T}{16}}$$

Answer

$$\frac{\mathrm{T}}{4}$$

Answer

$$\mathrm{\frac{T}{8}}$$

AC fundamentals

An alternating e.m.f. is $\mathrm{e}=\mathrm{e}_0 \sin \omega \mathrm{t}. In what time the e.m.f. will have half its maximum value, if '\mathrm{e}' starts from zero? (\mathrm{T}= time period, \sin 30^{\circ}=0.5$)

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