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

Question

A time varying current i is passed through a resistance R as shown in figure. The total heat generated in the resistance is (A) 11 i02 R t0 (B) 13 i02 R t0 (C) 17 i02 R t0 (D) 15 i02 R t0

Tardigrade Admin · Accepted Answer

Total heat produced = ∫ limits0t0((3 i0/t0) t)2 R d t+(3 i0)2 R(2 t0-t0)+i02 R(3 t0-2 t0) =3 i02 R t0+9 i02 R t0+i02 R t0=13 i02 R t0

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

$11 i_{0}^{2} R t_{0}$

$13 i_{0}^{2} R t_{0}$

$17 i_{0}^{2} R t_{0}$

$15 i_{0}^{2} R t_{0}$

Total heat produced $=$
$0 \int t_{0} (\frac{3 i _{0}}{t _{0}} t)^{2} R d t + (3 i_{0})^{2} R (2 t_{0} - t_{0}) + i_{0}^{2} R (3 t_{0} - 2 t_{0})$
$= 3 i_{0}^{2} R t_{0} + 9 i_{0}^{2} R t_{0} + i_{0}^{2} R t_{0} = 13 i_{0}^{2} R t_{0}$

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

11i02​Rt0​

13i02​Rt0​

17i02​Rt0​

15i02​Rt0​