If the r.m.s. current in an a.c. circuit is $5$ A, having frequency $50$ Hz. The value of current $\dfrac{1}{300}$ s after its value becomes zero (in A) is
$\{\sin(\pi/3) = (3)^{0.5}/2\}$

Question

If the r.m.s. current in an a.c. circuit is 5 A, having frequency 50 Hz. The value of current (1)/(300) s after its value becomes zero (in A) is \ (π/3) = (3)^ 0.5 /2\

Quantrex Academy · Accepted Answer

Correct answer: B. 5 (3)/(2)

The equation for alternating current is given by

I = I_0 \sin(\omega t)

.

Given

I_{rms} = 5

A, the peak current is:

I_0 = I_{rms}\sqrt{2} = 5\sqrt{2}

A

The angular frequency is:

\omega = 2\pi f = 2\pi \times 50 = 100\pi

rad/s

Substituting

t = \dfrac{1}{300}

s into the current equation:

I = 5\sqrt{2} \sin \lleft(100\pi \times \dfrac{1}{300})

I = 5\sqrt{2} \sin \left(\dfrac{\pi}{3}\right)

I = 5\sqrt{2} \times \dfrac{\sqrt{3}}{2}

I = 5\sqrt{\dfrac{3}{2}}

A

Answer:

5\sqrt{\dfrac{3}{2}}

If the r.m.s. current in an a.c. circuit is 5 A, having frequency...

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