Question

An alternating e.m.f. is given by e = e₀ sin ωt. In what time the e.m.f. will have value `e_0/sqrt 2`, if ‘e’ starts from zero?

`(sin 45^circ = 1/sqrt 2)`

Options

• `T/2 "second"`

• `T/4 "second"`

• `T/8 "second"`

• `T/12 "second"`

Answer 1

`bb(T/8 "second")`

Explanation:

e = e₀ sin ωt

`e/sqrt 2` = e = e₀ sin ωt    ...`(because e = e_0/sqrt 2)`

∴ sin ωt = `1/sqrt 2`

∴ sin ωt = `sin pi/4    ...(because sin pi/4 = 1/sqrt 2)`

∴ ωt = `pi/4`

∴ `(2 pi)/T t = pi/4`

∴ t = `T/8`