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 15s.

d q d t = t = 2 0 t + 8 t 2 ⇒ ∫ 0 q d q = ∫ 0 1 5 ( 2 0 t + 8 t 2 ) d t ⇒ q = 2 0 * 1 5 2 2 + 8 . 1 5 3 3 = 1 1 2 5 0 C

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 15s.

Option 1 - 2100C

Option 2 - 2250C

Option 3 - 260C

Option 4 - 11250C

2 Views|Posted 4 months ago

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Answered by

Vishal Baghel | Contributor-Level 10

4 months ago

Correct Option - 4

Detailed Solution:

$\frac{d q}{d t} = t = 20 t + 8 t^{2}$

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

$\Rightarrow q = 20 * \frac{1 5^{2}}{2} + 8 . \frac{1 5^{3}}{3} = 11250 C$

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