Question

The instantaneous current of an AC is given by $I=5\sin 314t$. What is the (i) peak value (ii)r.m.s. value (iii)frequency of current.

Answer 1

Hint: The rms value of AC is always lesser than the instantaneous value. The numerical value of the alternating current equation is the instantaneous value of current. Instantaneous value divided by square root of 2 gives rms value of current.

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

Complete step by step answer:
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.
We are given,
$I=5\sin 314t$, where I₀ =5 is the peak value of AC.
Therefore the peak value of AC is 5A
${{I}_{rms}}=\dfrac{{{I}_{0}}}{\sqrt{2}}=\dfrac{5}{\sqrt{2}}$
Therefore the r.m.s. value of AC is $\dfrac{5}{\sqrt{2}}$
To find frequency we need to find the time period of AC.
We are given $\omega =314$.
$T=\dfrac{2\pi }{\omega }=\dfrac{2\pi }{314}$$\dfrac{1}{T}=\dfrac{314}{2\pi }$
Frequency= $\dfrac{1}{T}=\dfrac{314}{2\pi }$
                 = 50 Hz
Therefore the frequency is 50 Hz.
Hence, the correct answer is option 50 Hz.

Additional Information
1. In a simple circuit, the current is found by dividing the voltage by the resistance. An AC current is calculated using the peak current (determined by dividing the peak voltage by the resistance), the angular frequency and the time.
2. Direct current (dc) refers to systems in which the source voltage is constant.
3. Alternating current (ac) refers to systems in which the source voltage varies periodically, particularly sinusoidally.
4. The voltage source of an AC system puts out 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 ${{I}_{0}}\succ {{I}_{rms}}.$ Time period of an AC is known as the time taken by the current to complete one oscillation.