Answer to Question #161286 in Electrical Engineering for Aliyu Auwal Gunda

Question

What is the average power dissipation in an RLC series circuit with R=10 ohm, L=0.1 H, C=10 MF, when driven at resonance by 100 V-RMS source

Answer 1

$P=I_{rms}\times U_{rms}$ ; $Z=\sqrt{R^2+(\frac{L}{\sqrt{LC}}-\frac{\sqrt{LC}}{C})^2}$

$I_{rms}=\frac{U_{rms}}{Z}=$ $\frac{U_{rms}}{\sqrt{R^2+(\frac{L}{\sqrt{LC}}-\frac{\sqrt{LC}}{C})}}$ $=\frac{100}{\sqrt{10^2+(\frac{0.1}{\sqrt{0.1\times10^{-2}}}-\frac{\sqrt{0.1\times10^{-2}}}{10^{-2}})^2}}=10$ A

$P=10\times100=1000$ W.