Question

A series AC circuit containing an inductor (20 mH), a capacitor ($120\mu F$) and a resistor ($60\Omega$) is driven by an AC source of 24 V/50 Hz. The energy dissipated in the circuit in 60 s is :

• A. $2.26\times {10}^{3}J$
• B. $3.39\times {10}^{3}J$
• C. $5.65\times {10}^{2}J$
• D. $5.17\times {10}^{2}J$

Answer 1

Answer: (D)

$5.17\times {10}^{2}J$

$R=60\Omega$ f = 50 Hz, $\omega =2\pi f=100\pi$

$x_C=\frac{1}{\omega C}=\frac{1}{100\pi \times 120\times {10}^{-6}}$

$x_C=26.52\Omega$

$x_L=\omega L=100\pi \times 20\times {10}^{-3}=2\pi \Omega$

$x_C-x_L=20.24\approx 20$

$z=\sqrt{R^2+(x_C-x_L{)}^2}$

$z=20\sqrt{10}\Omega$

$cos\varphi =\frac{R}{z}=\frac{3}{\sqrt{10}}$

$P_{avg}=VIcos\varphi ,I=\frac{v}{z}$

$P_{avg}=\frac{v^2}{z}cos\varphi$

$P_{avg}=8.64watt$

$Q=P.t=8.64\times 60=5.18\times {10}^2$