Time to Reach RMS Value in AC Current – Rankers Physics
Topic: Alternating Current
Subtopic: Average Current and RMS Current

Time to Reach RMS Value in AC Current

An ac current flowing in a circuit is given by \(i = i_0 sin \omega t\). The minimum time taken to reach zero to rms value of current is
\(\frac{\pi}{2\omega}\)
\(\frac{\pi}{4\omega}\)
\(\frac{\pi}{\omega}\)
\(\frac{2\pi}{\omega}\)

Solution:

The RMS value is \(i = \frac{i_0}{\sqrt{2}}\). Thus, \(\frac{i_0}{\sqrt{2}} = i_0 sin \omega t ⇒ \omega t = \frac{\pi}{4} ⇒ t = \frac{\pi}{4\omega}\).

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