A time varying current $i$ is passed through a resistance $R$ as shown in figure. The total heat generated in the resistance is
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Total heart produced
$ = \int_0^{{t_0}} {{{\left( {\frac{{3{i_0}}}{{{t_0}}}t} \right)}^2}} Rdt + {\left( {3{i_0}} \right)^2}R\left( {2{t_0} - {t_0}} \right) + i_0^2R\left( {3{t_0} - 2{t_0}} \right)$
$=3 i_{0}^{2} R t_{0}+9 i_{0}^{2} R t_{0}+i_{0}^{2} R t_{0}=13 i_{0}^{2} R t_{0}$
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