Physics - EMI/AC Question with Solution | TestHub

(Power factor), $P_f=\cos \varphi =\frac{R}{Z}$

Where $R,Z$ are the resistance and impedance respectively.
(Energy dissipated) $E=\frac{V_{rm\text{s}}^2}{Z}\times \cos \varphi \times t$
$\Rightarrow E=\frac{V_{rm\text{s}}^2}{Z}\times \frac{R}{Z}\times t$

$\Rightarrow E=\frac{V_{rm\text{s}}^2}{Z^2}\times R\times t$

$V_{rm\text{s}},t$ are the RMS voltage and time respectively.

We know that the Impedance of a LCR circuit is given by the formula,
$$\begin{gathered} Z^2=R^2+{\left(\omega L-\frac{1}{\omega \mathrm{C}}\right)}^2 \\ \Rightarrow Z^2=60^2+{\left(2\pi \times 50\times 20\times 10^{-3}-\left(\frac{1}{2\pi \times 50\times 120\times 10^{-6}}\right)\right)}^2 \end{gathered}$$

Where $\omega ,L,\mathrm{C}$ are the angular frequency, inductance and capacitance in the circuit respectively.
$\Rightarrow Z^2=60^2+{\left(2\pi -\frac{1000}{12\pi }\right)}^2$

$\Rightarrow Z^2=4009.7$

$\therefore E=\frac{24^2}{4009.7}\times 60\times 60\mathrm{J}$

$=517.14\mathrm{J}$

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