Question 19: AC fundamentals

Question

The instantaneous values of alternating current and voltages in a circuit are $\mathrm{I}=\frac{3}{\sqrt{2}} \sin (200 \pi t)$ ampere and $\mathrm{V}=\frac{3}{\sqrt{2}} \sin \left(200 \pi t+\frac{\pi}{6}\right)$ volt. What is the average power consumed in the circuit in watt ?

Accepted Answer

The average (real) power is given by
$$P_{m avg}=V_{m rms}\;I_{m rms}\cos\varphi$$
where
$I_m=	frac{3}{\sqrt2}$ and $V_m=	frac{3}{\sqrt2}$ are the amplitudes,
$\varphi=$ phase difference $=+	frac\pi6$,
$I_{m rms}=	frac{I_m}{\sqrt2}=	frac32$,
$V_{m rms}=	frac{V_m}{\sqrt2}=	frac32$.
So
$ P_{m avg} =\Bigl(	frac32\Bigr)\Bigl(	frac32\Bigr)\cos\!\Bigl(	frac\pi6\Bigr) =\frac{9}{4}\,\frac{\sqrt3}{2} =\frac{9\sqrt3}{8}\ {m W}. $
Answer:
$\displaystyle \frac{9\sqrt3}{8}$Ã¢ÂÂW
(Option D).

Answer

$\frac{\sqrt{3}}{8}$

Answer

$\frac{6 \sqrt{3}}{8}$

Answer

$\frac{8 \sqrt{2}}{9}$

Answer

$\frac{9 \sqrt{3}}{8}$

AC fundamentals

The instantaneous values of alternating current and voltages in a circuit are \mathrm{I}=\frac{3}{\sqrt{2}} \sin (200 \pi t) ampere and \mathrm{V}=\frac{3}{\sqrt{2}} \sin \left(200 \pi t+\frac{\pi}{6}\right) volt. What is the average power consumed in the circuit in watt ?

Choose the correct answer: