The effective (rms) voltage of a sine wave with a peak voltage of 200V is _____.

The effective (rms) voltage of a sine wave can be calculated using the relationship between the peak voltage and the rms voltage. For a sinusoidal wave, the rms voltage is equal to the peak voltage divided by the square root of 2. Specifically, the formula is:

[ V_{rms} = \frac{V_{peak}}{\sqrt{2}} ]

In this case, the peak voltage is given as 200V. Applying the formula:

[ V_{rms} = \frac{200V}{\sqrt{2}} \approx \frac{200V}{1.414} \approx 141.4V ]

Therefore, the effective (rms) voltage for a sine wave with a peak voltage of 200V is approximately 141.4 volts. This value is significant for HVACR systems as rms voltage is commonly used for evaluating the performance and safety of electrical components, as well as for calculating power usage. The understanding of rms voltage is crucial for ensuring that equipment operates efficiently and within safe limits.