FCC Exam Question: 3-6A5
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.
3-23C3
3-68K2
3-47F5
3-90O3
3-17B3
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Includes Elements 1, 3, 6, 7R, 8, and 9.