Question

The current in a conductor varies with time t as $I=2t+3t^2$ amp. where I is ampere and t in second. Electric charge flowing through a section of the conductor during $t=2sec$ to $t=3sec$ is:-

• A. $10C$
• B. $24C$
• C. $33C$
• D. $44C$

Answer 1

Answer: (B)

$\text{Step 1: Electric charge passing through the conductor}$

We know, Instantneous current across a conductor can be defined as:

$I=\frac{dQ}{dt}$

$\Rightarrow dQ=Idt$

$\Rightarrow dQ=(2t+3t^2)dt$ $....\left(1\right)$

$\text{Step 2: Integrate the above equation}$

Electric Charge flowing through section of the conductor during $t=2s$ to $t=3s$ can be obtained by integrating the equation $\left(1\right)$

$\int dQ={\int }_{t=2s}^{t=3s}(2t+3t^2)dt$

$\Rightarrow \Delta Q=2{\left[\frac{t^2}{2}\right]}_2^3+3{\left[\frac{t^3}{3}\right]}_2^3$

$\Rightarrow \Delta Q=[9-4]+[27-8]$$=24C$

Hence, Option B is correct