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Homework Statement
ac voltage
v=sinx
Homework Equations
how do you prove that rms voltage is 0.707v using integration
The formula for calculating rms voltage using integration is Vrms = √(1/T * ∫(0 to T) v(t)^2 dt), where T is the period of the voltage signal and v(t) is the instantaneous voltage at time t.
Integration is used to calculate rms voltage because it takes into account the entire voltage signal over a period of time, rather than just looking at the peak values. This provides a more accurate representation of the average voltage and is useful for AC signals that may vary over time.
The square root in the formula for rms voltage is used to find the root mean square (RMS) value of the voltage signal. This value represents the effective or equivalent DC value of the signal and is commonly used in electrical engineering calculations.
Yes, the integration method can be used for any type of voltage signal as long as the signal is periodic and has a well-defined period. This includes sinusoidal, square, and triangular waveforms.
One limitation of using integration to calculate rms voltage is that it assumes the voltage signal is continuous. If the signal is not continuous, then the integration method may not provide an accurate result. Additionally, the integration method may be more complex to use for non-periodic signals or signals with variable frequency.