Question

In the figure, the voltage are $V_1\left(t\right)=100cos\left(\omega t\right),V_2\left(t\right)=100cos(\omega t+\frac{\pi }{18})and{V}_3\left(t\right)=100cos(\omega t+\frac{\pi }{36})$. The circuit is in sinusoidal steady-state, and R<< $\omega L$. $P_1,P_{2}and{P}_3$ are the average power outputs. Which one of the following statements is true?

• A. $P_1=P_2=P_3=0$
• B. $P_1<0,P_2>0,P_3>0$
• C. $P_1<0,P_2>0,P_3<0$
• D. $P_1>0,P_2<0,P_3>0$

Answer 1

The correct option is C $P_1<0,P_2>0,P_3<0$


$V_2:\frac{\pi }{18}=\frac{{180}^0}{18}={10}^0$

$V_3:\frac{\pi }{36}=\frac{{180}^0}{36}=5^0$

$V_{2}leads{V}_{1}and{V}_3$,

So, $V_2$ is a source (delivers real power), $V_1$ and $V_3$ are sink(absorbs real power).

$Hence,P_2>0,P_1,P_3<0$