In the series LCR circuit as shown in figure, the heat developed in 80 seconds and amplitude of wattless current is:

 

$\begin{array}{c}\text{ Heat }={\left({\mathrm{i}}_{\mathrm{rms}}\right)}^2\cdot \mathrm{Rt}\\ {\mathrm{i}}_{\mathrm{rms}}=\frac{{\mathrm{i}}_0}{\sqrt{2}}=\frac{25}{\mathrm{Z}\sqrt{2}}\text{ where, }\mathrm{Z}=\sqrt{{\mathrm{R}}^2+{\left({\mathrm{x}}_{\mathrm{L}}-{\mathrm{x}}_{\mathrm{C}}\right)}^2}\\ =\sqrt{4^2+(7-4{)}^2}=5\mathrm{\Omega }\end{array}$

$\Rightarrow \text{ Heat }={\left(\frac{25}{5\sqrt{2}}\right)}^2\times 4\times 80=4000\mathrm{J}$ and 

Amplitude of wattless current = ${\mathrm{i}}_0\sin \mathrm{\varphi }$

where; $\mathrm{\varphi }={\tan }^{-1}\left(\frac{{\mathrm{x}}_{\mathrm{L}}-{\mathrm{x}}_{\mathrm{C}}}{\mathrm{R}}\right)={\tan }^{-1}\left(\frac{7-4}{4}\right)={37}^{\circ }$

$\Rightarrow$Amplitude $={\mathrm{i}}_0\sin {37}^{\circ }=\frac{25}{5}\times \frac{3}{5}=3\text{ ampere }$