First slide

Electrical power

Question

A time varying current i is passed through a resistance R as shown in figure. The total heat generated in the resistance is

Moderate

A

$11 i_{0}^{2} {Rt}_{0}$
B

$13 i_{0}^{2} {Rt}_{0}$
C

$17 i_{0}^{2} {Rt}_{0}$
D

$15 i_{0}^{2} {Rt}_{0}$

Solution

Total heat produced =
$\begin{array}{l} \int_{0}^{t_{0}} {(\frac{3 i_{0}}{t_{0}} t)}^{2} Rdt + {(3 i_{0})}^{2} R (2 t_{0} - t_{0}) + i_{0}^{2} R (3 t_{0} - 2 t_{0}) \\ = 3 i_{0}^{2} {Rt}_{0} + 9 i_{0}^{2} {Rt}_{0} + i_{0}^{2} {Rt}_{0} = 13 i_{0}^{2} {Rt}_{0} \end{array}$

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