Question

Choose the correct option.

If the rms current in a 50 Hz AC circuit is 5A, the value of the current 1/300 seconds after its value becomes zero is ______.

Options

• `5sqrt2 A`

• `5sqrt(3/2) A`

• `5/6 A`

• `5/sqrt2 A`

Answer 1

If the rms current in a 50 Hz AC circuit is 5A, the value of the current 1/300 seconds after its value becomes zero is `5sqrt(3/2) A`.

Explanation:

Substitute the given values from,

Frequency = `f - 50 Hz`  .....(1)

Current = `I = 5A` ......(2)

Time = `1/300 S`  .....(3)

Let `I_O` be the peak value

Therefore, `I_O = sqrt(2)I` .....(4)

Put the values in equation (2) and (4) and calculate:

`I_O = sqrt(2) xx 5`

`I_O = 5sqrt(2)A` ......(5)

∵ `I = I_0 sin(wt)`` ......(6)

Put the values in equations (3), (5) and (6) and calculate:

Also, `I = 5sqrt(2) xx sin(2pi f xx 1/300)`

`I = 5sqrt(2) xx sin(100pi xx 1/300)`

`I = 5sqrt(2) xx sin 60`

`I = 5sqrt(2) xx sqrt(3)/2`

`I = 5 xx sqrt(3)/sqrt(2) A`