Question

A current in a wire is given by the equation, $I = 2t^2 - 3t + 1$, the charge through cross section of wire in time interval $t = 3\, s$ to $t = 5\,s$ is

• A. $32.33\,C$
• B. $43.34\,C$
• C. $45.5\,C$
• D. $42\,C$

Answer 1

Answer: (B)

$43.34\,C$

Answer 2

As $I=\frac{dQ}{dt}$ ; $dQ-Idt$ ; $dQ=\left(2t^{2}-3t+1\right)dt$ $\int \,dQ=\int \limits ^{t=5}_{t=3}\,\left(2t^{2}-3t+1\right)dt$ ; $Q=\left[\frac{2t^{3}}{3}-\frac{3t^{2}}{2}+t\right]^{5}_{3}$ $=\left[\frac{2}{5}\left(125-27\right)-\frac{3}{2}\left(25-9\right)+2\right]$ $=43.34\,C$