A  $750Hz$, 20V source is connected to a resistance of  $100\Omega$, an inductance of 0.1803 Henry and a capacitance of 10 microfarad, all in series. The time in which the resistance (thermal capacity $=2joul/{}^{0}C$) will get heated by  ${10}^{0}C$ is 

$$\begin{gathered} \omega =2\pi f=2\times 3.14\times 750 \\ {X}_L=\omega L=2\times 3.14\times 750\times 0.1803 =849.2\Omega \\ {X}_C=\frac{1}{\omega C}=\frac{1}{2\times 3.14\times 750\times 10\times {10}^{-6}} =21.2\Omega \\ {X}_L-X_C=849.2-21.2\Rightarrow 828\Omega \\ Z=\sqrt{R^2+{(X_L-X_C)}^2} =\sqrt{{\left(100\right)}^2+{\left(828\right)}^2}=834\Omega \end{gathered}$$

$$\begin{gathered} but P=V_{rms}{I}_{rms}\cos \varphi \\ =\frac{V_{rms}^2}{Z^2}R=\frac{{\left(20\right)}^2\left(100\right)}{{\left(834\right)}^2}\Rightarrow 0.0575w \end{gathered}$$

And total energy Lost= Heat produced in resistor 

$$\begin{gathered} Pt=mS\Delta \theta \\ t=\frac{ms\Delta \theta }{P} =\frac{2\times 10}{0.0575}=348s\Rightarrow 5.8\min \end{gathered}$$