Q. A source of $e.m.f.\ E = 15\ V$ and having negligible internal resistance is connected to a variable resistance so that the current in the circuit increases with time as $i = 1.2\ t + 3.$ Then, the total charge that will flow in first five seconds will be
A) $10\ C$
B) $20\ C$
C) $30\ C$
D) $40\ C$
Explanation
(c) $i = \frac{dQ}{dt} \Rightarrow dQ = idt \Rightarrow Q = \int_{t_{1}}^{t_{2}}{idt = \int_{0}^{5}{(1.2t + 3)dt}}$
$= \left\lbrack \frac{1.2t^{2}}{2} + 3t \right\rbrack_{0}^{5} = 30C$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.