For the same peak value which of the following wave will ‘have the highest r.m.s. value?

Square wave
Half wave rectified sine wave
Triangular wave
Sine wave

The correct answer is: A. Square wave

The root mean square (RMS) value of a waveform is the square root of the average of the squares of the instantaneous values of the waveform. In other words, it is the effective value of the waveform, which is the value that would produce the same heating effect in a resistor as a direct current of the same value.

The RMS value of a sine wave is equal to its peak value divided by $\sqrt{2}$. This is because the sine wave is symmetrical about its mean value, so the positive and negative half-cycles are equal in area. The RMS value of a square wave is equal to its peak value. This is because the square wave is not symmetrical about its mean value, so the positive half-cycle has a larger area than the negative half-cycle. The RMS value of a half-wave rectified sine wave is equal to its peak value divided by $\sqrt{2}$. This is because the half-wave rectified sine wave is symmetrical about its mean value, but it only has one half-cycle. The RMS value of a triangular wave is equal to its peak value divided by $\sqrt{3}$. This is because the triangular wave is not symmetrical about its mean value, and its positive half-cycle has a larger area than its negative half-cycle.

Therefore, the square wave has the highest RMS value for the same peak value.