Question

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

$R=60\Omega f=50Hz,\omega =2\pi f=100\pi$
$x_C=\frac{1}{\omega C}=\frac{1}{100\pi \times 120\times 10^{-6}}$
$x_{C}26.52\Omega$
$x_L=\omega L=100\pi \times 20\times 10^{-3}=2\pi \Omega$
$x_C-x_L=20.24\approx 20$
$z=\sqrt{R^2+{\left(x_C-x_L\right)}^2}$
$z=20\sqrt{10}\Omega$
$\cos \varphi =\frac{R}{z}=\frac{3}{\sqrt{10}}$
$P_{avg}=VI\cos \varphi ,I=\frac{v}{z}$
$=\frac{v^2}{z}\cos \varphi$
$=8.64$ watt
$Q=P.t=8.64\times 60=5.18\times 10^2$