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Q.
A time varying current $i$ is passed through a resistance $R$ as shown in figure. The total heat generated in the resistance is
Current Electricity
Solution:
Total heat produced $=$
$\int\limits_{0}^{t_{0}}\left(\frac{3 i_{0}}{t_{0}} t\right)^{2} R d t+\left(3 i_{0}\right)^{2} R\left(2 t_{0}-t_{0}\right)+i_{0}^{2} R\left(3 t_{0}-2 t_{0}\right)$
$=3 i_{0}^{2} R t_{0}+9 i_{0}^{2} R t_{0}+i_{0}^{2} R t_{0}=13 i_{0}^{2} R t_{0}$
