If $E = 100 sin (100 t)$ volt and $I = 100 sin (100 t + \frac{π}{3}) m A$ are the instantaneous voltage and current, then the rms values of voltage and current are respectively

70.7 V

70.7 m A

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60.9 V

69.3 m A

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90.6 V

141.4 m A

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60 V

70 m A

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Solution

The correct option is A $70.7 V$ , $70.7 m A$
The instantaneous voltage is
$E = 100 sin (100 t)$ volt ....(i)
Compare it with $E = E_{0} sin (ω t)$ volt
We get
$E_{0} = 100$ volt, $ω = 100 r a d s^{- 1}$
The rms value of voltage is
$E_{r m s} = \frac{E_{0}}{\sqrt{2}} = \frac{100}{\sqrt{2}}$ volt $= 70.7 V$
The instantaneous value of current is
$I = 100 sin (100 t + \frac{π}{3}) m A$
Compare it with
$I = I_{0} sin (ω t + ϕ)$
We get,
$I_{0} = 100 m A$ , $ω = 100 r a d s^{- 1}$
The rms value of current is
$I_{r m s} = \frac{I_{0}}{\sqrt{2}} = \frac{100}{\sqrt{2}} m A = 70.7 m A$

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If E=100sin(100t) volt and I=100sin(100t+π3)mA are the instantaneous voltage and current, then the rms values of voltage and current are respectively

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