Question

The instantaneous value of current in an AC circuit is \[i = 2\sin \left( {100\pi t + \dfrac{\pi }{3}} \right)A\]. The current at the beginning (t=0) will be
(A) \[2\sqrt 3 A\]
(B) \[\sqrt 3 A\]
(C) \[\dfrac{{\sqrt 3 }}{2}A\]
(D) Zero

Answer 1

Hint: Instantaneous current is the amount of charge passing through a conductor at a moment of time, whereas the time-averaged current is the total amount of charge passing through a conductor in a time interval. The instantaneous value of an alternating voltage or current is the value of voltage and current at a particular instance of time.Alternating current is an electric current that periodically reverses its direction and continuously changes its magnitude with time.In this question, we need to calculate the initial current that is flowing in the circuit for which we have to just put the value of time as zero in the given instantaneous equation of the current to get the result.

Complete step by step answer:
The instantaneous current in AC circuit is given as:
\[i = 2\sin \left( {100\pi t + \dfrac{\pi }{3}} \right)A\]
Instantaneous current in an AC circuit gives the value of current at a moment of time or at an instance. Here the instantaneous value of current is to be calculated at the beginning, i.e.,
$t = 0$
Substitute $t = 0$ in the given instantaneous equation
\[i = 2\sin \left( {100\pi t + \dfrac{\pi }{3}} \right)A\] to determine the initial value of the current as:
\[\Rightarrow
i\left( t \right) = 2\sin \left( {100\pi t + \dfrac{\pi }{3}} \right) \\
\Rightarrow
i\left( 0 \right) = 2\sin \left( {100\pi \left( 0 \right) + \dfrac{\pi }{3}} \right) \\
\Rightarrow
= 2\sin \left( {\dfrac{\pi }{3}} \right) \\
\Rightarrow
= 2 \times \dfrac{{\sqrt 3 }}{2} \\
\Rightarrow
= \sqrt 3 {\text{ A}} \\
\]
Hence, the current in the circuit at the beginning will be \[{i_{\left( {t = 0} \right)}} = \sqrt 3 A\].
Hence,option (B) is the correct answer.

Note: The current at the beginning does not mean that the current was flowing in the circuit before the switch is ON but, it is the amount of the current flowing through the circuit as soon the circuit is closed with the switch or any other appropriate medium.