Question

The figure shows current varying with time. The magnitude of constant direct current for a particular time which would produce same heat in identical resistance as produced by given varying current in the seconds.

• A. 1 A when passed for 15 seconds
• B. $\frac{1}{3}$ A when passed for 15 seconds
• C. $\frac{\sqrt{5}}{3}$ A when passed for 3 seconds
• D. $\frac{\sqrt{5}}{9}$ A when passed for 3 seconds

Answer 1

Answer: (B), (C)

The correct options are
B

$\frac{1}{3}$ A when passed for 15 seconds

C

$\frac{\sqrt{5}}{3}$ A when passed for 3 seconds

Heat = $\int i^{2}Rdt={\int }_0^1(t{)}^{2}Rdt+{\int }_1^2{1}^{2}Rdt+{\int }_2^3(3-t{)}^{2}Rdt=\frac{1}{2}R+R+\frac{R}{3}=\frac{5R}{3}{I}^{2}R\times 3=\frac{5R}{3},I^2=\frac{5}{9}Aand{I}^{2}R\times 15=\frac{5R}{3},I_2=\frac{1}{3}A$