**A current through a wire depends on time as i = α _{0}t + βt^{2} where α_{0} = 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

**A current through a wire depends on time as i = α _{0}t + βt^{2} where α_{0} = 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

**Correct Answer is B) 11250 C **

**Explaination ::**

we have ,

**i = α _{0}t + βt^{2}** ,

**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**