What is the effective (rms) voltage of a sine wave with a peak voltage of 200V?

What is the effective (rms) voltage of a sine wave with a peak voltage of 200V?

• A. 100
• B. 120.5
• C. 141.4
• D. 200

Answer: (C)

The effective (rms) voltage of a sine wave is calculated using the relationship between the peak voltage and the rms voltage. For a sine wave, the rms voltage is derived by multiplying the peak voltage by a specific factor, which is approximately 0.7071 (or 1 divided by the square root of 2). In this case, with a peak voltage of 200V, the calculation to find the rms voltage would be: rms Voltage = Peak Voltage × 0.7071 rms Voltage = 200V × 0.7071 ≈ 141.4V This value, 141.4V, represents the effective voltage, which provides a measure of the work done by the voltage in an AC circuit, equivalent to a DC voltage that would deliver the same power to a resistor. The rms value is crucial for calculating power in AC systems because AC current fluctuates both positively and negatively, and the rms value accounts for this variation to give a meaningful measure of voltage in practical applications. Other choices do not represent the correct conversion from peak voltage to effective voltage as defined for sine waves, thereby confirming that 141.4V is indeed the appropriate answer.

The effective (rms) voltage of a sine wave is calculated using the relationship between the peak voltage and the rms voltage. For a sine wave, the rms voltage is derived by multiplying the peak voltage by a specific factor, which is approximately 0.7071 (or 1 divided by the square root of 2).

In this case, with a peak voltage of 200V, the calculation to find the rms voltage would be:

rms Voltage = Peak Voltage × 0.7071

rms Voltage = 200V × 0.7071 ≈ 141.4V

This value, 141.4V, represents the effective voltage, which provides a measure of the work done by the voltage in an AC circuit, equivalent to a DC voltage that would deliver the same power to a resistor. The rms value is crucial for calculating power in AC systems because AC current fluctuates both positively and negatively, and the rms value accounts for this variation to give a meaningful measure of voltage in practical applications.

Other choices do not represent the correct conversion from peak voltage to effective voltage as defined for sine waves, thereby confirming that 141.4V is indeed the appropriate answer.