Question 351: AC fundamentals

Question

In an a.c. circuit $\mathrm{I}=100 \sin 200 \pi \mathrm{t}$. The time required for the current to achieve its peak value will be

Accepted Answer

The given current in the a.c. circuit is expressed as :
$$ I = 100 \sin(200 \pi t). $$
To determine the time required for the current to achieve its peak value, we need to analyze the sinusoidal function $\sin(200 \pi t)$. The peak value of a sine function occurs when the argument of the sine function is an odd multiple of $\frac{\pi}{2}$ (i.e., $\frac{\pi}{2}$, $\frac{3\pi}{2}$, etc.).
Since we are interested in the first peak, we consider :
$$ 200 \pi t = \frac{\pi}{2}. $$
Solving for $t$ gives :
Divide both sides by $200 \pi$ :
$$ t = \frac{\pi/2}{200 \pi} = \frac{1}{400}. $$
Therefore, the time required for the current to achieve its first peak value is :
$ \frac{1}{400} \, 	ext{seconds}. $
The correct option is D : $\frac{1}{400} \, \mathrm{s}$.

Answer

$\frac{1}{100} \mathrm{~s}$

Answer

$\frac{1}{200} \mathrm{~s}$

Answer

$\frac{1}{300} \mathrm{~s}$

Answer

$\frac{1}{400} \mathrm{~s}$

AC fundamentals

In an a.c. circuit \mathrm{I}=100 \sin 200 \pi \mathrm{t}. The time required for the current to achieve its peak value will be

Choose the correct answer: