Question

Power dissipated in an $LCR$ series circuit connected to an a.c. source of emf $\varepsilon$ is :

• A. $\varepsilon^{2} R / \sqrt{ R ^{2}+\left( L \omega-\frac{1}{ C \omega}\right)^{2}}$
• B. $\varepsilon^{2} R /\left[ R ^{2}+\left( L \omega-\frac{1}{ C \omega}\right)^{2}\right]$
• C. $\varepsilon^{2} \sqrt{\left[R^{2}+\left(L \omega-\frac{1}{C \omega}\right)^{2}\right]} / R$
• D. $\frac{\varepsilon^{2}\left[ R ^{2}+\left(L \omega-\frac{1}{ C \omega}\right)^{2}\right]}{ R }$

Answer 1

Answer: (B)

$\varepsilon^{2} R /\left[ R ^{2}+\left( L \omega-\frac{1}{ C \omega}\right)^{2}\right]$

Answer 2

$P _{ av } = E _{ rms } \cdot I _{ rms } \cos \phi$
$=\varepsilon \cdot \frac{\varepsilon}{ z } \cdot \frac{ R }{ z }=\frac{\varepsilon^{2} R }{ z ^{2}}$
$=\frac{\varepsilon^{2} R }{ R ^{2}+\left(\omega L -\frac{1}{\omega C }\right)^{2}}$