Question

If the instantaneous current in a metallic wire is $i=\left(5+10t\right)A$ then find amount of charge flown through it from $t=2s$ to $t=3s$ is

• A. 10 C
• B. 20 C
• C. 30 C
• D. 40 C

Answer 1

The correct option is C 30 C

Given instantaneous current,

$i=(5+10t)A$

and from the definition of instantaneous current, $i=\frac{dq}{dt}$

$\Rightarrow (5+10t)=\frac{dq}{dt}$

$dq=(5+10t)dt$

Integrating implies,

$Q=5t+{5t}^2$

At $t=2$,

$Q_1=30C$

At $t=3$,

$Q_2=60C$

$\therefore$ Option (C) is the correct option.