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Exercise:
Show that the root mean square value of a sinusoidal voltage signal vt V_ sinomega t is sscVrms fracV_sqrt

Solution:
The rms value corresponds to the square root of the average value of the square of the voltage signal over one period. The average can be calculated as sscV^rms _^T v^t textdt _^T V_^ sin^omega t textdt There are several ways to find a value for the egral: abcliste abc Using the identiy sin^omega t frac-cos omega t we find _^T sin^omega t textdt frac_^T left - cos omega tright textdt fracleft_^T textdt - _^T cos omega t textdt right frac left leftt right_^T - leftfracsin omega t omega right_^T right abc abcliste
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Exercise:
Show that the root mean square value of a sinusoidal voltage signal vt V_ sinomega t is sscVrms fracV_sqrt

Solution:
The rms value corresponds to the square root of the average value of the square of the voltage signal over one period. The average can be calculated as sscV^rms _^T v^t textdt _^T V_^ sin^omega t textdt There are several ways to find a value for the egral: abcliste abc Using the identiy sin^omega t frac-cos omega t we find _^T sin^omega t textdt frac_^T left - cos omega tright textdt fracleft_^T textdt - _^T cos omega t textdt right frac left leftt right_^T - leftfracsin omega t omega right_^T right abc abcliste
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Branches
Electrodynamics
Tags
ac circuit, integral, power, rms, root mean square
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Difficulty
(2, default)
Points
0 (default)
Language
ENG (English)
Type
Calculative / Quantity
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