Subelement A: Principles— Topic 6: Electrical Measurements
Question 3-6A5
Element 3 (GROL)By what factor must the voltage measured in an AC circuit, as indicated on the scale of an AC voltmeter, be multiplied to obtain the average voltage value?
Explanation
An AC voltmeter typically measures the Root Mean Square (RMS) voltage of a sinusoidal waveform. The average voltage for a single half-cycle of a sine wave (the full-cycle average is zero) is found by multiplying the peak voltage by 2/π.
To convert the RMS voltage (what the meter shows) to the average voltage:
1. First, convert RMS to peak voltage: Peak Voltage = RMS Voltage × √2 (approximately 1.414).
2. Then, convert peak to average voltage: Average Voltage = Peak Voltage × (2/π) (approximately 0.637).
3. Combining these: Average Voltage = (RMS Voltage × √2) × (2/π) = RMS Voltage × (2√2 / π).
Calculating (2√2 / π) ≈ (2 × 1.414) / 3.14159 ≈ 2.828 / 3.14159 ≈ 0.9.
Therefore, you must multiply the RMS voltage reading by approximately 0.9 to obtain the average voltage value.
A) 0.707 is the factor to convert peak voltage to RMS voltage (1/√2).
B) 1.414 is the factor to convert RMS voltage to peak voltage (√2).
D) 3.14 is the value of π, not a direct multiplication factor in this context.
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