The charge flowing through a resistor $R$ varies with time $t$ as $Q = 3t -6t^2.$ The heat produced in $R$ till the current in it becomes zero is
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$\mathrm{i}=\frac{\mathrm{d} Q}{\mathrm{dt}}=3-12 \mathrm{t}$
$t=\frac{1}{4} \sec$
$\mathrm{H}-\int_{0}^{1 / 4}(3-12 \mathrm{t})^{2} \times \mathrm{Rdt}$
$=\left.\frac{(3-12 t)^{2}}{3 x-12}\right|_{0} ^{1 / 4} R$
$=\frac{+1}{36}[27]=\frac{3 \mathrm{R}}{4}$
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