Question

An R-L-C circuit containing a 52 $\Omega$ resistor, a 230 mH inductor and a 8.8 $\mu$F capacitor is driven by an AC voltage source that has an amplitude of 150 V and frequency f = 80Hz. How much average power is dissipated by this circuit?

• A. 78.6 W
• B. 0
• C. 19.6 W
• D. 24.8 W

Answer 1

The correct option is A 78.6 W

$X_L=2\pi fL=2\times \pi \times 80\times 230\times {10}^{-3}=115.6$ $\Omega$

$X_C=\frac{1}{2\pi fC}=\frac{1}{2\pi \times 80\times 8.8\times {10}^{-6}}=226$ $\Omega$

$i_{rms}=\frac{V_{rms}}{\sqrt{R^2+(X_L-X_C{)}^2}}=\frac{150}{\sqrt{(52{)}^2+(110.4{)}^2}}=\frac{150}{122}$

$P_{avg}=V_{rms}{I}_{rms}\cos \varphi =150\times \frac{150}{122}\times \frac{R}{\sqrt{R^2+(X_L-X_C{)}^2}}=\frac{150}{{122}^2}\times 150\times 52=78.6$ $W$