A current through a wire depends on time as i = α0t + βt2 where α0 = 20 A/s and β = 8 As-2. Find the charge crossed through a section of the wire in 15 s.

more_vert

A current through a wire depends on time as i = α0t + βt2 where α0 = 20 A/s and β = 8 As-2. Find the charge crossed through a section of the wire in 15 s.

a. 2100 C

b.11250 C

c. 2250 C

d. 260 C

more_vert

verified

Correct Answer is B) 11250 C

Explaination ::

we have ,

i = α0t + βt2  , α = 20 A/s and β = 8As-2 ,t = 15 sec

We know that ,

$$i={ {dq\over dt}⇒ { \int_0^t idt}=\int_0^Q dq }$$

$$⇒ { \int_0^{15} (α_0t + βt^2)dt}={\int_0^Q dq }$$

$$Q=[ { {α_0t ^2\over2}+{ βt^3\over 3}}]_0^{15}$$

$$Q = 20×15×{15 \over 2 }+ 8×15×15×{15 \over3} – 0$$

Q = 11250 C