A current through a wire depends on time as i =α0 t +β t 2 where α0=20 A / s and β=8 As -2 . Find the charge crossed through a section of the wire in 15 s.

Question

A current through a wire depends on time as i =α0 t +β t 2 where α0=20 A / s and β=8 As -2 . Find the charge crossed through a section of the wire in 15 s. (A) 2250 C (B) 11250 C (C) 2100 C (D) 260 C

Tardigrade Admin · Accepted Answer

i =20 t +8 t 2 i =( dq / dt ) ⇒ ∫ d q =∫ idt ⇒ q =∫ limits015(20 t +8 t 2) dt q =((20 t 2/2)+(8 t 3/3))015 q =10 ×(15)2+(8(15)3/3) q =2250+9000 q =11250 C

Q. A current through a wire depends on time as $i = α_{0} t + β t^{2}$ where $α_{0} = 20 A / s$ and $β = 8 A s^{- 2} .$ Find the charge crossed through a section of the wire in $15 s$ .

$2250 C$

$11250 C$

$2100 C$

$260 C$

$i = 20 t + 8 t^{2}$
$i = \frac{d q}{d t}$
$\Rightarrow \int d q = \int i d t$
$\Rightarrow q = 0 \int 15 (20 t + 8 t^{2}) d t$
$q = (\frac{20 t ^{2}}{2} + \frac{8 t ^{3}}{3})_{0}^{15}$
$q = 10 \times (15)^{2} + \frac{8 ( 15 ) ^{3}}{3}$
$q = 2250 + 9000$
$q = 11250 C$

Q. A current through a wire depends on time as i=α0​t+βt2 where α0​=20A/s and β=8As−2. Find the charge crossed through a section of the wire in 15s.

2250C

11250C

2100C

260C