At any instant t the values of voltage applied and the current through a series LCR circuit are given as:

$V=\frac{1}{\sqrt{2}} \sin (100 \pi t) V$

$I=\frac{1}{\sqrt{2}} \sin (100 \pi t+\frac{\pi}{3}) A$

The average power consumed in the circuit is given by:

$\frac{1}{8} W$

The correct answer is Option (1) → $\frac{1}{8} W$

To find the average power consumed in a circuit, 

$P_{avg}=V_{rms}I_{rms}\cos\phi$

Given,

$V=\frac{1}{\sqrt{2}}\sin(100πt)$

$I=\frac{1}{\sqrt{2}}\sin\left(100πt+\frac{π}{3}\right)$

$V_{rms}=\frac{V_0}{\sqrt{2}}=\frac{1}{\sqrt{2}.\sqrt{2}}=\frac{1}{2}$

$I_{rms}=\frac{I_0}{\sqrt{2}}=\frac{1}{\sqrt{2}.\sqrt{2}}=\frac{1}{2}$

$∴P_{avg}=\left(\frac{1}{2}\right)\left(\frac{1}{2}\right)\cos\left(\frac{π}{3}\right)$

$=\left(\frac{1}{2}\right)^3=\frac{1}{8} W$