Question

The equation for an alternating current is given by i = 77 sin 314t. find the frequency, time period and instantaneous current value at t = 2 ms.

Answer 1

Answer:

154sq cm

Explanation:

since it is i × t

=77×2

=154sq cm

Answer 2

Answer of each solution is given below .

Given :

Equation for an alternating current , i = 77 sin (314 t)    .....( 1 )

We need to find its frequency .

So, angular frequency , $\omega = 314\ rad/s$ .

Therefore , frequency ,

$f=\dfrac{\omega}{2\pi}\\\\f=\dfrac{314}{2\times 3.14}\\\\f=50\ Hz$

We also know the relation between time period and frequency is :

$T=\dfrac{1}{f}\\\\T=\dfrac{1}{50}\ s\\\\T=0.02\ s$

Now , we need to find the value of current at time , t = 2 ms = 0.02 s .

Putting value of t = 0.02 s in above equation .

We get ,

$i = 77 \times sin (314\times 0.02) \\\\i = 0 \ A.$  ( Since , $sin (314\times 0.02)= 0$  )

Hence , this is the required solution .

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Alternating current

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