Question

The rms value of a.c with peak value of \(200\) V is

• A. \(100\,\text{V}\)
• B. \(\frac{200}{\sqrt{2}}\,\text{V}\)
• C. \(300\,\text{V}\)
• D. \(200\sqrt{2}\,\text{V}\)
• E. \(\frac{200}{\sqrt{3}}\,\text{V}\)

Hint:

Always remember: \(V_{\text{rms}} = \frac{V_0}{\sqrt{2}}\) for sinusoidal AC signals.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
The root mean square (rms) value of an alternating current (AC) or voltage is a measure of its effective value. For a sinusoidal AC voltage, the rms value is related to the peak (or maximum) value of the voltage by a specific factor.
Step 2: Key Formula or Approach:
The relationship between the rms value (\( V_{rms} \)) and the peak value (\( V_{peak} \) or \( V_0 \)) of a sinusoidal AC voltage is given by:
\[ V_{rms} = \frac{V_{peak}}{\sqrt{2}} \] Step 3: Detailed Explanation:
We are given:
- The peak value of the AC voltage, \( V_{peak} = 200 \) V.
We need to find the rms value, \( V_{rms} \).
Using the formula:
\[ V_{rms} = \frac{V_{peak}}{\sqrt{2}} \] Substitute the given peak value:
\[ V_{rms} = \frac{200}{\sqrt{2}} \text{ V} \] This can also be rationalized by multiplying the numerator and denominator by \( \sqrt{2} \):
\[ V_{rms} = \frac{200\sqrt{2}}{2} = 100\sqrt{2} \text{ V} \] However, the option is given in the un-rationalized form.
Step 4: Final Answer:
The rms value is \( \frac{200}{\sqrt{2}} \) V. This corresponds to option (B).