A current through a wire depends on time as i = α 0t + β t2 where α 0 = 20 A/s and β = 8 As ⁻². Find the charge crossed through a section of the wire in 15 s. (a) 2250 C (b) 2100 C (c) 260 C (d) 11250 C

Answer: (d). Current i = α₀ t + β t² q = ∫₀¹⁵ i dt = α₀ t²2 + β t³3 q = (20 × 225)/(2) + (8 × 3375)/(3) = 2250 + 9000 q = 11250 C, so the answer is (d).

A current through a wire depends on time as i = α 0t + β t2 where α 0… | JEE Main 2021 (24 Feb, Shift 1)

Q19JEE Main 2021 · 24 FEB · SHIFT 1Easy

Electric Current, Drift Velocity & Current Density

A current through a wire depends on time as

i = $\alpha$ 0t + $\beta$ t2

where $\alpha$ 0 = 20 A/s and $\beta$ = 8 As ${}^{-2}$ . Find the charge crossed through a section of the wire in 15 s.

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Answer: (d)

Current $i = \alpha_0 t + \beta t^{2}$
$q = \int_0^{15} i\,dt = \dfrac{\alpha_0 t^{2}}{2} + \dfrac{\beta t^{3}}{3}$
$q = \dfrac{20 \times 225}{2} + \dfrac{8 \times 3375}{3} = 2250 + 9000$
$q = 11250\text{ C}$ , so the answer is (d).

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Electric Current, Drift Velocity & Current Density question from JEE Main 2021 (24 Feb, Shift 1)

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