The current through the resistor increases steadily from 5A to 15A in 10 seconds. what charge

The current through the resistor increases steadily from 5A to 15A in 10 seconds. what charge passed through the resistor during this time.

Task data: I1 (initial current in the resistor) = 5 A; I2 (end current) = 15 A; Δt (duration of current rise) = 10 s.

1) The current strength after 10 s is expressed by the formula t: I = I0 + k * t, whence, according to the conditions of the problem, k = (I – I0) / t = (15 – 5) / 10 = 1 and I = t.

2) Charge passed: q = 010∫ Idt = 010∫ tdt = t ^ 2/2 = 10 ^ 2/2 = 50 Cl.

Answer: In 10 seconds, a charge of 50 C passed through the resistor.