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Question Number 173515 by Muktarr last updated on 12/Jul/22

Answered by aleks041103 last updated on 12/Jul/22

U_(rms) =(√((1/T)∫_0 ^( T) U^2 (t)dt))  U(t)= { ((+10, 0<t<T/2)),((−10, T/2<t<T)) :}  ⇒U^2 (t)=100=const.  ⇒U_(rms) =(√((1/T)∫_0 ^T 100dt))=10  ⇒U_(rms) =10V

$${U}_{{rms}} =\sqrt{\frac{\mathrm{1}}{{T}}\int_{\mathrm{0}} ^{\:{T}} {U}^{\mathrm{2}} \left({t}\right){dt}} \\ $$$${U}\left({t}\right)=\begin{cases}{+\mathrm{10},\:\mathrm{0}<{t}<{T}/\mathrm{2}}\\{−\mathrm{10},\:{T}/\mathrm{2}<{t}<{T}}\end{cases} \\ $$$$\Rightarrow{U}^{\mathrm{2}} \left({t}\right)=\mathrm{100}={const}. \\ $$$$\Rightarrow{U}_{{rms}} =\sqrt{\frac{\mathrm{1}}{{T}}\int_{\mathrm{0}} ^{{T}} \mathrm{100}{dt}}=\mathrm{10} \\ $$$$\Rightarrow{U}_{{rms}} =\mathrm{10}{V} \\ $$

Commented by Tawa11 last updated on 13/Jul/22

Great sir.

$$\mathrm{Great}\:\mathrm{sir}. \\ $$

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