Q. A source of emf E=15V and having negligible internal resistance, is connected to a variable resistance, so that the current in the circuit increases with time as I=1.2t+3. Then, the total charge that will flow in first 5s will be
A) 10C
B) 20C
C) 30C
D) 40C
Explanation
(c) Charge (q) is given by
$q = \int_{}^{}{Idt}$
Given$,\ \ \ \ I = 1.2t + 3$
Integrating the expression using
$\int_{}^{}{x^{n}\ dx = \frac{x^{n + 1}}{n + 1}}$
We have
$q = \int_{}^{}{Idt = 1.2\ \int_{}^{}{t\ dt + 3\int_{}^{}{dt}}}$
$q = 1.2\left\lbrack \frac{t^{2}}{2} \right\rbrack_{0}^{5} + 3\lbrack t\rbrack_{0}^{5}$
$q = \frac{1.2}{2} \times 25 + 3 \times 5$
$q = 15 + 15 = 30C$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.