Question

The instantaneous value of current in an a.c. circuit is \(I = 2 \sin \left[ 100\pi t + \frac{\pi}{3} \right]\) A. The current will be maximum for the first time at \((\sin 90^\circ = 1)\)

• A. \(\frac{1}{100}\text{ s}\)
• B. \(\frac{1}{200}\text{ s}\)
• C. \(\frac{1}{400}\text{ s}\)
• D. \(\frac{1}{600}\text{ s}\)

Hint:

AC max condition: $\sin(\theta)=1 \Rightarrow \theta=\frac{\pi}{2}$

Answer 1

The Correct Option is D

Concept: Maximum current when: \[ 100\pi t + \frac{\pi}{3} = \frac{\pi}{2} \]

Step 1: Solve. \[ 100\pi t = \frac{\pi}{2} - \frac{\pi}{3} = \frac{3\pi - 2\pi}{6} = \frac{\pi}{6} \]

Step 2: \[ t = \frac{1}{600} \text{ s} \] Final Answer: Option (D)