The AC circuit is shown below.

Here,$R=100, X_L=L\omega =0.1803\times 750\times 2\mathrm{\pi }=850\mathrm{\Omega }$

The capacitive reactance $X_{\mathrm{c}}=\frac{1}{\mathrm{C\omega }}=\frac{1}{{10}^{-5}\times 2\mathrm{\pi }\times 750}=21.23 \mathrm{\Omega }$

Total impedance $\mathrm{Z}=\sqrt{{\mathrm{R}}^2+{\left(X_{\mathrm{L}}-X_{\mathrm{C}}\right)}^2}$

$=\sqrt{{100}^2+{\left(850-21.23\right)}^2}=834.77\approx 835$

The heat loss $\mathrm{H}={\mathrm{i}}_{\mathrm{rms}}^2\mathrm{Rt}=\left(\mathrm{ms}\right)∆\mathrm{t}$

$\frac{20}{835}\times \frac{20}{835}\times 100\mathrm{t}=\left(2\right)\times 10$

$\mathrm{t}=348.61 \sec$