Question

A source of emf $E=15\,V$ and having negligible internal resistance, is connected to a variable resistance, so that the current in the circuit increases with time as $ I=1.2t+3 $ . Then, the total charge that will flow in first $ 5\,s $ will be

• A. 10 C
• B. 20 C
• C. 30 C
• D. 40 C

Answer 1

Answer: (C)

Charge $(q)$ is given by
$q=\int I d t$
given, $ I=1.2 t+3$
Integrating the expression using
$\int x^{n} d x=\frac{x^{n+1}}{n+1}$
we have $q=\int I d t=1.2 \int t d t+3 \int d t$
$q=1.2\left[\frac{t^{2}}{2}\right]_{0}^{5}+3[t]_{0}^{5}$
$q=\frac{1.2}{2} \times 25+ 3 \times 5$
$q=15+15=30\, C$