A current in a wire is given by the equation, I = 2t2 - 3t + 1, the charge through cross section of wire in time interval t = 3 s to t = 5 s is

Question

A current in a wire is given by the equation, I = 2t2 - 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

Tardigrade Admin · Accepted Answer

As I=(dQ/dt) ; dQ-Idt ; dQ=(2t2-3t+1)dt ∫ dQ=∫ limits t=5t=3 (2t2-3t+1)dt ; Q=[(2t3/3)-(3t2/2)+t]53 =[(2/5)(125-27)-(3/2)(25-9)+2] =43.34 C

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

$32.33 C$

$43.34 C$

$45.5 C$

$42 C$

As $I = \frac{d Q}{d t}$ ;
$d Q - I d t$ ;
$d Q = (2 t^{2} - 3 t + 1) d t$
$\int d Q = t = 3 \int t = 5 (2 t^{2} - 3 t + 1) d t$ ;
$Q = [\frac{2 t ^{3}}{3} - \frac{3 t ^{2}}{2} + t]_{3}^{5}$
$= [\frac{2}{5} (125 - 27) - \frac{3}{2} (25 - 9) + 2]$
$= 43.34 C$

Q. A current in a wire is given by the equation, I=2t2−3t+1, the charge through cross section of wire in time interval t=3s to t=5s is

32.33C

43.34C

45.5C

42C