Question

The instantaneous value of an AC is given by $I=5\sin (wt+\phi )amp$ . The rms value of current is
\[\begin{align}
  & A)5A \\
 & B)\dfrac{5}{\sqrt{2}}A \\
 & C)5\sqrt{2}A \\
 & D)2.5A \\
\end{align}\]

Answer 1

Hint: We must know that the rms value of AC is always lesser than the instantaneous value. Also, the numerical value of the alternating current equation is the instantaneous value of current. The rms value of an alternating current is given by dividing the Instantaneous value with square root of 2.

Formula used:
${{I}_{rms}}=\dfrac{{{I}_{0}}}{\sqrt{2}}$

Complete step by step answer:
We know that Alternating Current (AC) is an electric current which in intervals reverses direction and changes its magnitude continuously with time in contrast to direct current (DC) which flows only in one direction.
Generally, instantaneous value of an AC is represented in the form as,
 $I={{I}_{0}}\sin (wt+\phi )amp$
Now, we are given with,
$I=5\sin (wt+\phi )amp$
Where \[{{I}_{0}}=5A\] is the maximum value of AC.
$\begin{align}
  & {{I}_{0}}\succ {{I}_{rms}}. \\
 & {{I}_{rms}}=\dfrac{{{I}_{0}}}{\sqrt{2}}=\dfrac{5}{\sqrt{2}}A \\
\end{align}$
Therefore, the rms value of this AC current is $\dfrac{5}{\sqrt{2}}A$. So the answer is option (b).

Additional information:
1. In a simple circuit, the current flowing through the circuit is found by dividing the voltage by the resistance. But, AC current is calculated using the peak current (determined by dividing the peak voltage by the resistance), the angular frequency and the time.
2. In a DC circuit, Direct current (DC) refers to systems in which the source voltage is constant.
3. In a system with alternating current (AC), the source voltage varies periodically, particularly sinusoidally.
4. The voltage source of an AC system gives a voltage that is calculated from the time, the peak voltage, and the angular frequency.

Note:
The possibility of the mistake is that you may choose option (c). You might get confused with the formula to be ${{I}_{0}}=\dfrac{{{I}_{rms}}}{\sqrt{2}}$ . This is incorrect. The method of remembering the formula is to keep in mind that ${{I}_{0}}\succ {{I}_{rms}}$ .