Question

Derive the RMS value of a 2Vpp:

A) Sine Wave
B) Square Wave
C) Sawtooth Wave
D) All of the Above

Answer 1

According to this statement option D) All of the Above is correct.

Step-by-step explanation:

The Root Mean Square (RMS) value of a signal is a measure of its effective or average value, taking into account both the magnitude and duration of the signal. For a sine wave, the RMS value is given by the formula
`\( V_(rms) = (V_(pp))/(√(2)) \)`, where
`\( V_(pp) \)` is the peak-to-peak voltage. Applying this formula to a 2Vpp sine wave yields
`\( V_(rms) = (2)/(√(2)) = √(2) \) V.`

For a square wave with peak-to-peak voltage
`\( V_(pp) \)`, the RMS value is
`\( V_(rms) = (V_(pp))/(√(2)) \)`. Given a 2Vpp square wave, the RMS value would be
`\( V_(rms) = (2)/(√(2)) = √(2) \) V`, which is consistent with the sine wave result.

The RMS value of a sawtooth wave is also determined by
`\( V_(rms) = (V_(pp))/(√(2)) \)`. Therefore, for a 2Vpp sawtooth wave, the RMS value is
`\( V_(rms) = (2)/(√(2)) = √(2) \)`V. Since the RMS value is the same for all three waveforms, the answer is D) All of the Above. This demonstrates a commonality in the RMS calculation for these periodic waveforms, irrespective of their shapes.