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The current in a conductor varies with time according to i = α₀t + βt², where α₀ = 20 A s⁻¹ and β = 8 A s⁻². Determine the total charge that passes through a cross-section of the wire in 15 s.

1. 2250 C
2. 11250 C
3. 2100 C
4. 260 C

Correct answer: 11250 C

Solution

Q = integral_0^15 (20t + 8t^2) dt = 10t^2 + (8/3)t^3 at t=15 = 2250 + 9000 = 11250 C.

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