The r.m.s. value and mean value is the same in the case of

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square wave

Explanation: For a square wave, the instantaneous magnitude is constant at either $+V_m$ or $-V_m$ throughout the conduction period. Consequently, the root-mean-square (r.m.s.) value and the average (mean) value are identical to the peak value $V_m$.

Working Principle: In a square wave, the squaring of the instantaneous value results in a constant $V_m^2$. The mean of this constant value is $V_m^2$, and the square root of that mean is $V_m$. Similarly, the average value of a symmetrical square wave is simply $V_m$ because the magnitude is constant over the entire half-cycle.

Key Formulas: $V_{rms} = \sqrt{\frac{1}{T} \int_{0}^{T} v(t)^2 dt}$ — Definition of RMS value; $V_{avg} = \frac{1}{T} \int_{0}^{T} |v(t)| dt$ — Definition of Average value; $V_{rms} = V_{avg} = V_m$ — Condition for Square Wave

Key Points: A square wave has a Form Factor (FF) of 1.; Form Factor is defined as the ratio of RMS value to Average value.; For sine waves, FF = 1.11; for triangular waves, FF = 1.15.

Advantages: Simplifies power calculation in switching circuits.; Ideal for digital signal processing.

Disadvantages: High harmonic content compared to sine waves.; Causes significant EMI due to fast rise/fall times.

Applications: Pulse Width Modulation (PWM) in inverters.; Digital clock signals.

Additional Info: For a sine wave, RMS = $V_m / \sqrt{2} \approx 0.707 V_m$ and Average = $2V_m / \pi \approx 0.637 V_m$.. For a triangular wave, RMS = $V_m / \sqrt{3} \approx 0.577 V_m$ and Average = $V_m / 2 = 0.5 V_m$.

Answer: C is correct — The square wave is the only standard waveform where the magnitude remains constant, resulting in an RMS value equal to the average value.

Exam Tip: Always remember: Form Factor = (RMS Value / Average Value). If the waveform is a square wave, Form Factor is 1, which implies RMS = Average.

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