In an AC (alternating current) system, the voltage alternates in both polarity and amplitude over time. The RMS (root mean square) value of the voltage is a way to represent the effective or equivalent DC (direct current) voltage that would produce the same heating effect in a resistive load.
When we say that the positive and negative voltages on AC are equal in amplitude, we mean that the peak amplitudes of the positive and negative voltage cycles are the same. However, the RMS value takes into account the mathematical average of the squared values of the voltage waveform over a complete cycle.
The reason why the RMS voltage value is not zero, even when the positive and negative voltages have equal amplitudes, is due to the mathematical nature of calculating the RMS value.
Consider a sinusoidal AC voltage waveform. The instantaneous voltage values during the positive half of the cycle are positive, while during the negative half of the cycle, they are negative. Squaring these instantaneous voltage values makes them positive, and then taking the average (mean) of these squared values gives the RMS value.
Since squaring a negative number yields a positive number, the squared values during the negative half-cycle contribute positively to the RMS value. Consequently, even though the positive and negative voltages have equal amplitudes, their squared values are still positive, leading to a non-zero RMS value.
In summary, the RMS value represents the effective or equivalent DC voltage that produces the same heating effect as the AC voltage. It is not zero because squaring the negative voltages during the negative half-cycle contributes positively to the overall average, resulting in a non-zero RMS value.