A current through a wire depends on time as $i=\alpha_{0} t+\beta t^{2}$ Where $\alpha_{0}=20 \mathrm{~A} / \mathrm{s}$ and $\beta=8 A s^{-2}$. Find the charge crossed through a section of the wire in 15s.

JEE Main · 2021 · 24 Feb 2021 · Shift 1 · Current Electricity

A current through a wire depends on time as

i = α_{0} t + β t^{2}

Where

α_{0} = 20 A / s

and

β = 8 A s^{- 2}

. Find the charge crossed through a section of the wire in 15s.

Answer: (D)

The charge is found by integrating the current over time:

q = \int_{0}^{15} i d t = \int_{0}^{15} (20 t + 8 t^{2}) d t

q = [10 t^{2} + \frac{8 t ^{3}}{3}]_{0}^{15} = 10 (225) + \frac{8 ( 3375 )}{3} = 2250 + 9000 = 11250 C

JEE Main · 2021 · 24 Feb 2021 · Shift 1 · Single correct option