Question

An alternating e.m.f. is given by e = e₀ sin ωt. In what time the e.m.f. will have half its maximum value, if 'e' starts from zero? (T = Time period)

`(sin 30^circ = cos 60^circ = 0.5, cos 30^circ = sin 60^circ = sqrt3/2)`

Options

• `"T"/4`

• `"T"/16`

• `"T"/12`

• `"T"/8`

Answer 1

`"T"/12`

Explanation:

e = e₀ sin ωt

`"e"_0/2 = "e"_0`sin ωt

`1/2` = sin 30° = sin ωt

`sin pi/6 = sin omega"t" = sin (2pi"t")/"T"`

∴ `pi/6 = (2pi"t")/"T"`

∴ t = `"T"/12`