Question 36: AC fundamentals

Question

The instantaneous values of alternating current and voltages in a circuit given as
$$\begin{aligned}
& i=\frac{1}{\sqrt{2}} \sin (100 \pi t) \mathrm{amp} \
& e=\frac{1}{\sqrt{2}} \sin (100 \pi t+\pi / 3) 	ext { volt }
\end{aligned}$$
The average power (in watts) consumed in the circuit is

Accepted Answer

Given,
$$i=\frac{1}{\sqrt{2}} \sin (100 \pi t) \mathrm{amp}$$
and $$e=\frac{1}{\sqrt{2}} \sin (100 \pi t+\pi / 3)$$ volt
$$\Rightarrow \quad i_0=\frac{1}{\sqrt{2}}$$ and $$e_0=\frac{1}{\sqrt{2}}$$
We know that, average power,
$$\begin{aligned}
P_{\mathrm{av}}= & V_{\mathrm{rms}} 	imes i_{\mathrm{rms}} \cos \phi=\frac{1}{2} 	imes \frac{1}{2} 	imes \cos 60^{\circ} \
& \left(\because i_{\mathrm{rms}}=i_0 / \sqrt{2} 	ext { and } V_{\mathrm{rms}}=V_0 / \sqrt{2}ight) \
= & \frac{1}{2} 	imes \frac{1}{2} 	imes \frac{1}{2}=\frac{1}{8} \mathrm{~W}
\end{aligned}$$

Answer

$$\frac{1}{4}$$

Answer

$$\frac{\sqrt{3}}{4}$$

Answer

$$\frac{1}{2}$$

Answer

$$\frac{1}{8}$$

AC fundamentals

The instantaneous values of alternating current and voltages in a circuit given as $\begin{aligned} & i=\frac{1}{\sqrt{2}} \sin (100 \pi t) \mathrm{amp} \\ & e=\frac{1}{\sqrt{2}} \sin (100 \pi t+\pi / 3) \text { volt } \end{aligned}$ The average power (in watts) consumed in the circuit is

Choose the correct answer: