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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 15 s.

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2100 C

2250 C

260 C

11250 C

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detailed solution

Correct option is D

dqdt=20t+8t2⇒∫dq=∫015 20t+8t2dt⇒Δq=20t22+8t33015 =20×(15)22+8×(15)33=11250C

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A current through a wire depends on time as i=α0t+βt2 where α0=20A/s and β=8As−2. Find the charge crossed through a section of the wire in 15 s.

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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 15 s.