Question

The current flowing through an ac circuit is given by \(I = 5 \;sin\;(120πt)\;A\). How long will the current take to reach the peak value starting from zero?

• A. \(\frac{1}{60} s\)
• B. \(60 \;s\)
• C. \(\frac{1}{120} s\)
• D. \(\frac{1}{240}s\)

Answer 1

The Correct Option is D

To find how long the current will take to reach its peak value starting from zero, we first need to understand the mathematical expression given for current in the AC circuit.

The current is described by the function:

\(I = 5 \sin(120\pi t) \, A\)

This is a standard expression for oscillating current where:

• The amplitude is 5 A, indicating the peak current.
• The angular frequency (\omega) is 120\pi.

We aim to find the time taken by the sine function to reach its peak value from zero. A sine function (\sin(\theta)) reaches its maximum value of 1 at \(\theta = \frac{\pi}{2}\). Therefore, we need to set up the equation:

\(\omega t = \frac{\pi}{2}\)

Substitute the angular frequency:

\(120\pi t = \frac{\pi}{2}\)

Now, solve for t:

t = \frac{\pi}{2} \times \frac{1}{120\pi}\)

t = \frac{1}{240} \, \text{s}

Therefore, the time taken by the current to reach its peak value from zero is \(\frac{1}{240}\, \text{s}.

Conclusion: The correct answer is \(\frac{1}{240}\, \text{s}\).