Question 299: AC fundamentals

Question

The instantaneous value of current in an a.c. circuit is $I=3 \sin \left(50 \pi t+\frac{\pi}{4}\right) \mathrm{A}$. The current will be maximum for the first time at

Accepted Answer

Given equation of instantaneous current:
$$ I = 3 \sin \left(50\pi t + \frac{\pi}{4}ight) 	ext{ A} $$
The current will be
maximum
when the value of $\sin$ is $1$.
So,
$$ 50\pi t + \frac{\pi}{4} = \frac{\pi}{2} $$
Now, solve for $t$:
$ 50\pi t + \frac{\pi}{4} = \frac{\pi}{2} $
Subtract $\frac{\pi}{4}$ from both sides:
$ 50\pi t = \frac{\pi}{2} - \frac{\pi}{4} $
$ 50\pi t = \frac{2\pi - \pi}{4} $
$ 50\pi t = \frac{\pi}{4} $
Divide both sides by $50\pi$:
$ t = \frac{\pi}{4} \div 50\pi $
$ t = \frac{1}{4} 	imes \frac{1}{50} $
$ t = \frac{1}{200} 	ext{ s} $
Correct option is:
Option C
$\boxed{\frac{1}{200}~\mathrm{s}}$

Answer

$\frac{1}{50} \mathrm{~s}$

Answer

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

Answer

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

Answer

$\frac{1}{600} \mathrm{~s}$

AC fundamentals

The instantaneous value of current in an a.c. circuit is I=3 \sin \left(50 \pi t+\frac{\pi}{4}\right) \mathrm{A}. The current will be maximum for the first time at

Choose the correct answer: