In the conductor, within 10 seconds, with a uniform increase in the current strength

In the conductor, within 10 seconds, with a uniform increase in the current strength from 0 to 2 A, an amount of heat of 6 kJ was released. find the resistance of the conductor.

Data: t (elapsed time) = 10 s; I1 (initial current) = 0 A; I2 (end current) = 2 A; Q (released heat) = 6 kJ = 6 * 103 J.

1) The law of current change in the specified conductor: I (t) = x * t + y;

a) Current in the conductor I1 = 0 A: I (0) = x * 0 + y = 0, whence y = 0;

b) Current in the conductor I2 = 2 A: I (10) = x * 10 + y = x * 10 + 0 = 2, whence x = 2/10 = 0.2.

c) Law: I (t) = 0.2t + 0 = 0.2t.

2) Heat release: Q = 010∫ I ^ 2 * R * dt = R * 010∫ (0.2t) ^ 2 dt = R * 010∫ 0.04t ^ 2 dt = R * 0.04 * t3 / 3 | 010 = R * 0.04 * t3 / 3 | 010 = R * 0.04 * 10 ^ 3/3 = 13.33 (3) R.

3) Resistance: R = Q / 13.33 (3) = 6 * 10 ^ 3 / 13.33 (3) = 450 Ohm.

Answer: The resistance of the specified conductor is 450 ohms