Current Electricity Question 12
Question 12 - 2024 (29 Jan Shift 1)
The electric current through a wire varies with time as $I=I _0+\beta$ t. where $I _0=20 A$ and $\beta=3 A / s$. The amount of electric charge crossed through a section of the wire in $20 s$ is :
(1) $80 C$
(2) $1000 C$
(3) $800 C$
(4) $1600 C$
Show Answer
Answer: (2)
Solution:
Given that
Current $I=I _0+\beta t$
$I _0=20 A$
$\beta=3 A / s$
$I=20+3 t$
$\frac{dq}{dt}=20+3 t$
$\int _0^{q} dq=\int _0^{20}(20+3 t) dt$
$q=\int _0^{20} 20 d t+\int _0^{20} 3 t d t$
$q=\left[20 t+\frac{3 t^{2}}{2}\right] _0^{20}=1000 C$
