Q. A current through a wire depends on time $t\ as\ i = 10 + 4t.$ The charge crossing through the section of the wire in 10 s is
A) 50 C
B) 300 C
C) 400 C
D) 4C
Explanation
(b) $i = \frac{dQ}{dt} = 10 + 4t\ or\ dQ = (10 + 4)dt$
Integrating it, we get $Q = 10t + \frac{4t^{2}}{2} = 10t + 2t^{2}$
When $t = 10s,\ Q = 10 \times 10 + 2 \times 10^{2} = 300\ C$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.