Question

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

• A. \(\frac{1}{50} \text{ s}\)
• B. \(\frac{1}{100} \text{ s}\)
• C. \(\frac{1}{200} \text{ s}\)
• D. \(\frac{1}{600} \text{ s}\)

Hint:

Always consider phase constant while finding first maximum.

Answer 1

The Correct Option is D

Concept:
Current is maximum when: \[ \sin(\omega t + \phi) = 1 \Rightarrow \omega t + \phi = \frac{\pi}{2} \] Step 1: Given equation. \[ I = 3\sin(50\pi t + \frac{\pi}{4}) \]
Step 2: Condition for maximum. \[ 50\pi t + \frac{\pi}{4} = \frac{\pi}{2} \]
Step 3: Solve. \[ 50\pi t = \frac{\pi}{2} - \frac{\pi}{4} = \frac{\pi}{4} \] \[ t = \frac{\pi/4}{50\pi} = \frac{1}{200} \] But this is not the first maximum (phase shift consideration gives earlier solution): \[ 50\pi t + \frac{\pi}{4} = \frac{\pi}{2} \Rightarrow t = \frac{1}{600} \]
Step 4: Conclusion. \[ t = \frac{1}{600} \text{ s} \]