Question

A 10$\Omega$ resistance is connected across 220 V - 50 Hz AC supply. The time taken by the current to change from its maximum value of the rms value is:

• A. 2.5 ms
• B. 4.5 ms
• C. 3.0 ms
• D. 1.5 ms

Answer 1

Answer: (A)

2.5 ms

Answer 2

For an AC circuit, the current is given by

$I = I_0 \cos(\omega t)$

At the rms value,

$I = \frac{I_0}{\sqrt{2}}$

So,

$\cos(\omega t) = \frac{1}{\sqrt{2}} \quad \Rightarrow \quad \omega t = \frac{\pi}{4}$

Since $\omega = 2\pi f$ and $f = 50\, \text{Hz}$, we have

$\omega = 100\pi \, \text{rad/s}$

Thus,

$t = \frac{\pi/4}{100\pi} = \frac{1}{400} \, \text{s} = 2.5\,\text{ms}$