• # question_answer An LCR circuit of $R=100\,\Omega$ is connected to an AC source 100 V, 50 Hz. the magnitude of phase difference between current and voltage is ${{30}^{o}}$. The power dissipated in the LCR circuit is : A)  50 W                            B)  $86.6$ W C)  100 W                          D)  200 W

Average power dissipated in an AC circuit, ${{P}_{av}}={{V}_{rms}}\,{{I}_{rms}}\,\cos \phi$     ?(i) Where, the term $\cos \phi$ is known as power factor Given ${{V}_{rms}}=100\,V,\,\,R=100\Omega ,\,\phi =\,{{30}^{0}}$ $\therefore \,\,{{I}_{rms}}\,=\frac{{{V}_{rms}}}{R}=\frac{100}{100}=1A$ Putting the values in eq. (i) we get ${{P}_{av}}\,=100\times 1\,\times \,\cos {{30}^{0}}$ $=100\frac{\sqrt{3}}{2}$ $=50\,\sqrt{3}\,=86.6\,w$