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

0.7 V, 70.7 mA

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70.7 V, 70.7 mA

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141.4V, 141.4 mA

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100V, 100mA

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Solution

The correct option is B 70.7 V, 70.7 mA
The instantaneous value of voltage is
$V = 100 s i n (100 t) v o l t$
Compare it with, $V = V_{0} s i n (ω t)$ volt
We get $V_{0} = 100 V, ω = 100 r a d s^{- 1}$
The rms value of voltage is
$V_{r m s} = \frac{V_{0}}{\sqrt{2}} = \frac{100}{\sqrt{2}} = 70.7 V$
The instantaneous value of current is
I = 100sin $[100 t + \frac{π}{3}]$ mA
Compare it with, $I = I_{0} s i n (ω t + ϕ)$
We get $I_{0}$ = 100 mA, $ω$ = 100 rad $s^{-} 1$
The rms value of current is
$I_{r m s} = \frac{I_{0}}{\sqrt{2}} = \frac{100}{\sqrt{2}} = 70.7 m A$

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

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