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If \mathrm{ V = 100 sin (100t) V}  and   \mathrm{I}=100 \sin \left(100 \mathrm{t}+\frac{\pi}{3}\right) \mathrm{mA} are the instantaneous values of voltage and current, then the rms values of voltage and current are respectively:

Option: 1

70.7 V, 70.7 mA


Option: 2

70.7 V,70.7 A


Option: 3

141.4 V, 141.4 mA


Option: 4

100 V, 100 mA


Answers (1)

best_answer

The instantaneous value of voltage is
V=100 \sin (100 t) V
Compare it with
\mathrm{V}=\mathrm{V}_0 \sin (\omega \mathrm{t}) \mathrm{V}
We get
\mathrm{V}_0=100 \mathrm{~V}, \omega=100 \mathrm{rads}^{-1}
The rms value of voltage is 
\mathrm{V}_{\mathrm{rms}}=\frac{\mathrm{V}_0}{\sqrt{2}}=\frac{100}{\sqrt{2}} \mathrm{~V}=70.7 \mathrm{~V}
The instantaneous value of current is \mathrm{ I=100 \sin \left(100 t+\frac{\pi}{3}\right) \mathrm{mA}}
Compare it with \mathrm{ \mathrm{I}=\mathrm{I}_0 \sin (\omega \mathrm{t}+\phi)}
We get \mathrm{ \mathrm{I}_0=100 \mathrm{~mA}, \omega=100 \mathrm{rads}^{-1}}
The rms value of current is
\mathrm{ \mathrm{I}_{\mathrm{rms}}=\frac{\mathrm{I}_0}{\sqrt{2}}=\frac{100}{\sqrt{2}} \mathrm{~mA}=70.7 \mathrm{~mA}}

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