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iamnew
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Homework Statement
ac voltage
v=sinx
Homework Equations
how do you prove that rms voltage is 0.707v using integration
Prove rms voltage using integration
- Thread starter iamnew
- Start date
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- Tags
- Integration Rms Voltage
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SUMMARY
The discussion focuses on proving that the root-mean-square (RMS) voltage of the AC voltage function \( v = \sin x \) is 0.707 volts through integration. The RMS value is defined as the square root of the average of the square of the function over a specified interval. The relevant formula for calculating the average of the square of a function \( f(x) \) is given by \( \frac{\int_{t_{1}}^{t_{2}} (f(x))^{2} dx}{t_{2} - t_{1}} \). Participants are encouraged to perform the integration for \( f(x) = \sin x \) to arrive at the RMS value.
PREREQUISITES- Understanding of root-mean-square (RMS) calculations
- Familiarity with integration techniques
- Knowledge of sinusoidal functions
- Basic calculus concepts
- Perform integration of \( \sin^2 x \) over the interval [0, π] to calculate RMS voltage
- Explore the derivation of RMS values for other sinusoidal functions
- Study the application of RMS voltage in electrical engineering
- Learn about the differences between RMS and average voltage calculations
Students in electrical engineering, physics learners, and anyone interested in understanding the mathematical proof of RMS voltage for sinusoidal functions.
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