Question

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

विकल्प

• `5sqrt(2)` A

• `5sqrt(3/2)` A

• `5/6` A

• `5/sqrt(2)` A

Answer 1

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

Explanation:

Equation for i and V: Alternating current or voltage varying as sine function can be written as

`i = i_0 sin ωt = i_0 sin 2piv t = i_0 sin  (2pi)/T t`

And `V = V_0 sin ωt = V_0 sin 2pivt = V_0 sin  (2pi)/T t`

Where I and V are instantaneous values of current and voltage,

i₀ and V₀ are peak values  of current and voltage

ω = Angular frequency on rad/sec, v = Frequency in Hz 

T = TIme peroid

`I_(ωt) = I = sqrt(2)I_0 = 5sqrt(2)A`

`I = I_0 sin ωt`

At `t = 1/300  sec, I = 5sqrt(2) sin 2 pivt = 5sqrt(2) sin  2pi xx 50 xx 1/300`

= `5sqrt(2) sin  pi/3 = 5sqrt(2) sin 60^circ`

= `52 - sqrt(3)sqrt(2)` = 532

= `5sqrt(3/2) A`