Question

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

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

Hint:

The phase difference between $I_{max}$ and $I_{rms}$ is always $45^\circ$ ($\pi/4$ rad). The time taken is always $T/8$.

Answer 1

The Correct Option is A

Step 1: Current equation: $i = I_0 \cos(\omega t)$ (starting from max).
Step 2: We want $i = I_{rms} = \frac{I_0}{\sqrt{2}}$. $\frac{I_0}{\sqrt{2}} = I_0 \cos(\omega t) \implies \cos(\omega t) = \frac{1}{\sqrt{2}} \implies \omega t = \frac{\pi}{4}$.
Step 3: $t = \frac{\pi}{4\omega} = \frac{\pi}{4(2\pi f)} = \frac{1}{8f} = \frac{1}{8 \times 50} = \frac{1}{400} \text{ s} = 2.5 \text{ ms}$.