Question

An alternating voltage is given by E = 100 sin`(omega + pi/6)"V"`. The voltage will be maximum for the first time when is ______. [T = periodic time]

Options

• `"T"/12`

• `"T"/2`

• `"T"/6`

• `"T"/3`

Answer 1

An alternating voltage is given by E = 100 sin`(omega + pi/6)"V"`. The voltage will be maximum for the first time when is `underline("T"/6)`.

Explanation:

Given, alternating voltage is

E = 100 sin`(omega"t" + pi/6)`V

The voltage will be maximum, when

`sin(omega"t" + pi/6) = 1`

`=> sin(omega"t" + pi/6) = sin  pi/2`

`=> omega"t" + pi/6 = pi/2`

`=> omega"t" = pi/3`

`"t" = pi/(3omega) = (pi xx "T")/(3 xx 2pi)   ...[because omega = (2pi)/"T"]`

`= "T"/6`

Thus, the voltage will be maximum for the first time when t = `"T"/6`.