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7. Alternating current — Physics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 SciencePhysics7. Alternating current1 Mark
MCQ
An alternating voltage is given by : $e = e_1\, \sin \omega t + e_2\, \cos \omega t$. Then  the root mean square value of voltage is given by :-
  • A
    $\sqrt {e_1^2 + e_2^2}$
  • B
    $\sqrt {e_1e_2}$
  • C
    $\sqrt {\frac{e_1e_2}{2}}$
  • ✓
    $\sqrt {\frac{e_1^2 + e_2^2}{2}}$
✓

Answer

Correct option: D.
$\sqrt {\frac{e_1^2 + e_2^2}{2}}$
d
$\mathrm{V}_{\mathrm{rms}}^{2} =\int_{0}^{\mathrm{T}} \frac{\left(\mathrm{e}_{1} \sin \omega \mathrm{t}+\mathrm{e}_{2} \cos \omega \mathrm{t}\right)^{2} \mathrm{dt}}{\mathrm{T}}$

$=\sqrt{\frac{\mathrm{e}_{1}^{2}+\mathrm{e}_{2}^{2}}{2}}$

where $\omega=\frac{2 \pi}{\mathrm{T}}$

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