Subelement B: Electrical Math— Topic 12: Waveforms
Question 3-12B5
Element 3 (GROL)What is the RMS value of a 340-volt peak-to-peak pure sine wave?
Explanation
To determine the RMS (Root Mean Square) value of a pure sine wave, first find its peak voltage. A 340-volt peak-to-peak sine wave means the voltage swings from +170V to -170V. Therefore, the peak voltage (from zero to the maximum) is 340 V / 2 = 170 V.
The RMS value of a sine wave is the effective voltage, equivalent to a DC voltage that would dissipate the same amount of power in a resistive load. For a pure sine wave, the RMS voltage is calculated by dividing the peak voltage by the square root of 2 (approximately 1.414), or by multiplying the peak voltage by 0.707.
So, 170 V (peak) * 0.707 = 120.19 V. This rounds to 120 volts AC.
Option A (170 volts AC) represents the peak voltage, not the RMS value. Options B and D are incorrect calculations for the RMS value from the given peak-to-peak voltage.
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