Question

An AC source rated $220V,50Hz$ is connected to a resistor. The time taken by the current to change from its maximum to the rms value is:

• A. $0.25ms$
• B. $25ms$
• C. $2.5ms$
• D. $2.5s$

Answer 1

The correct option is C

$2.5ms$

Step 1. Given data

The total time taken to complete one cycle is $T=\frac{1}{f}$

frequency, $f$ $=50Hz$

Step 2. Finding the time from maximum to RMS value

The phase difference between the maximum and RMS value is $\frac{\mathrm{\pi }}{4}$

$\omega t=\frac{\mathrm{\pi }}{4}$ [$\omega$ is angular frequency, $t$ is time ]

$2\mathrm{\pi ft}=\frac{\mathrm{\pi }}{4}$

$t=\frac{1}{8f}$

$$\begin{gathered} t=\frac{1}{8x50Hz} \\ t=\frac{1}{400} \\ t=2.5ms \end{gathered}$$

Hence, option $\left(C\right)$ is correct.