Question

A \(50\,\mathrm{Hz}\) sinusoidal voltage has a peak value of \(141\,\mathrm{V}\). Its RMS value is

• A. \(70.7\,\mathrm{V}\)
• B. \(100\,\mathrm{V}\)
• C. \(141\,\mathrm{V}\)
• D. \(200\,\mathrm{V}\)

Hint:

For a sinusoidal voltage, \[ \boxed{ V_{\mathrm{rms}}=\frac{V_{\mathrm{max}}}{\sqrt2} } \] and \[ \boxed{ V_{\mathrm{max}}=\sqrt2\,V_{\mathrm{rms}}. } \]

Answer 1

The Correct Option is B

Step 1: Use the relation between peak and RMS values. For a sinusoidal waveform, \[ V_{\mathrm{rms}} = \frac{V_{\mathrm{max}}}{\sqrt{2}}. \] Given, \[ V_{\mathrm{max}}=141\,\mathrm{V}. \]

Step 2: Calculate the RMS value. \[ V_{\mathrm{rms}} = \frac{141}{\sqrt{2}} \approx \frac{141}{1.414} \approx100\,\mathrm{V}. \] Hence, \[ \boxed{100\,\mathrm{V}} \] Therefore, \[ \boxed{(B)} \] is the correct answer.