Question

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

• A. 70.7 V, 70.7 mA
• B. 70.7 V, 70.7 A
• C. 141.4 V, 141.4 mA
• D. 100 V, 100 mA

Answer 1

Answer: (A)

70.7 V, 70.7 mA

Answer 2

: The instantaneous value of voltage is

$V = 100\sin(100t)V$

Compare it with

$V = V_{0}\sin(\omega t)V$

we get

$V_{0} = 100V,\omega = 100rads^{- 1}$

The rms value of voltage is,

$V_{rms} = \frac{V_{0}}{\sqrt{2}} = \frac{100}{\sqrt{2}}V = 70.7V$

The instantaneous value of current is

$I = 100\sin\left( 100t + \frac{\pi}{3} \right)mA$

Compare it with

$I = I_{0}\sin(\omega t + \varphi)$

we get

$I_{0} = 100mA,\omega = 100rads^{- 1}$

The rms value of current is

$I_{rms} = \frac{I_{0}}{\sqrt{2}} = \frac{100}{\sqrt{2}}mA = 70.7mA$