Question

What is the minimum time required for $50Hz$. A.C to change its value from zero to rms value?

• A. $0.5ms$
• B. $1.5ms$
• C. $2.5ms$
• D. $3.5ms$

Answer 1

The correct option is C $2.5ms$

One cycle of A.C represented by $i=i_0\sin \omega t$ is shown in the figure below.

Angular frequency of A.C $\omega =\frac{2\pi }{T}=2\pi f$

RMS value of current $=\frac{i_0}{\sqrt{2}}$

Let $i=\frac{i_0}{\sqrt{2}}$ for time $t=t_1$
$\frac{i_0}{\sqrt{2}}=i_0\sin \omega t_1$
$\Rightarrow \omega t_1=\frac{\pi }{4}$
$\Rightarrow 2\pi f{t}_1=\frac{\pi }{4}$
$\Rightarrow t=\frac{1}{400}s=2.5ms$