The effective (rms) voltage of a sine wave with a peak voltage of 200V is what?

The effective (rms) voltage of a sine wave with a peak voltage of 200V is what?

• A. 100V
• B. 141.4V
• C. 200V
• D. 280V

Answer: (B)

To find the effective (rms) voltage of a sine wave, you use the relationship between the peak voltage (V_peak) and the rms voltage (V_rms). For a sine wave, the rms voltage is calculated by dividing the peak voltage by the square root of 2. The formula is: V_rms = V_peak / √2. In this case, with a peak voltage of 200V, you would calculate the rms voltage as follows: V_rms = 200V / √2 ≈ 200V / 1.414 ≈ 141.4V. This means the effective voltage that can be used for power calculations or equipment ratings is about 141.4 volts. This value represents the average power delivered by the sine wave, equating it to a DC voltage that would produce the same amount of heat in a resistor. Thus, 141.4V is the correct answer for the rms value of the sine wave with a peak voltage of 200V.

To find the effective (rms) voltage of a sine wave, you use the relationship between the peak voltage (V_peak) and the rms voltage (V_rms). For a sine wave, the rms voltage is calculated by dividing the peak voltage by the square root of 2.

The formula is:

V_rms = V_peak / √2.

In this case, with a peak voltage of 200V, you would calculate the rms voltage as follows:

V_rms = 200V / √2 ≈ 200V / 1.414 ≈ 141.4V.

This means the effective voltage that can be used for power calculations or equipment ratings is about 141.4 volts. This value represents the average power delivered by the sine wave, equating it to a DC voltage that would produce the same amount of heat in a resistor. Thus, 141.4V is the correct answer for the rms value of the sine wave with a peak voltage of 200V.