The electric current through a wire varies with time as where and The amount of electric charge crossed through a section of the wire in 20 sec is

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Solution

Q.
The electric current through a wire varies with time as $I = I_{0} + β t$ where $I_{0} = 20 A$ and $β = 3 A / s .$ The amount of electric charge crossed through a section of the wire in 20 sec is [2024]

1 80 C

2 1000 C

3 800 C

4 1600 C

Ans.
(2)

Given that, current $I = I_{0} + β t$

Also, $I_{0} = 20 A$ and $β = 3 A / s$

Hence, $d q / d t = 20 + 3 t \Rightarrow d q = (20 + 3 t) d t$

$\int_{0}^{q} d q = \int_{0}^{20} (20 + 3 t) d t$

$\Rightarrow q = {[20 t + \frac{3 t^{2}}{2}]}_{0}^{20} = 1000 C$

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