Question 132: AC fundamentals

Question

An alternating current is represented by the equation,
$i=100 \sqrt{2} \sin (100 \pi t)$ ampere. The RMS value of current and the frequency of the given alternating current are

Accepted Answer

To solve the problem, we need to determine both the RMS value of the current and the frequency from the given equation:
$$i(t)=100\sqrt{2}\sin(100\pi t).$$
Here's how we do it step by step:
RMS Current Calculation:
For a sinusoidal current of the form $$i(t)=I_0 \sin(\omega t),$$ the RMS (root-mean-square) current is given by:
$$I_{	ext{RMS}} = \frac{I_0}{\sqrt{2}}.$$
In our case, the amplitude $$I_0 = 100\sqrt{2}\, 	ext{A}.$$ Plugging into the formula:
$$I_{	ext{RMS}} = \frac{100\sqrt{2}}{\sqrt{2}} = 100\, 	ext{A}.$$
Frequency Calculation:
The argument of the sine function is $$100\pi t.$$ In the general form $$\sin(\omega t),$$ $$\omega$$ is the angular frequency which relates to the frequency $$f$$ by the equation:
$$\omega = 2\pi f.$$
Given $$\omega = 100\pi,$$ we can solve for $$f$$:
$$f = \frac{\omega}{2\pi} = \frac{100\pi}{2\pi} = 50\, 	ext{Hz}.$$
With these calculations, we find that the RMS current is $$100\, 	ext{A}$$ and the frequency is $$50\, 	ext{Hz}.$$
Thus, the correct option is:
Option D: $$100\,	ext{A}, \, 50\,	ext{Hz}.$$

Answer

$\frac{100}{\sqrt{2}} \mathrm{~A}, 100 \mathrm{~Hz}$

Answer

$50 \sqrt{2} \mathrm{~A}, 50 \mathrm{~Hz}$

Answer

$100 \sqrt{2} \mathrm{~A}, 100 \mathrm{~Hz}$

Answer

$100 \mathrm{~A}, 50 \mathrm{~Hz}$

AC fundamentals

An alternating current is represented by the equation, i=100 \sqrt{2} \sin (100 \pi t) ampere. The RMS value of current and the frequency of the given alternating current are

Choose the correct answer: