Question

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. 10 C
• B. 20 C
• C. 30 C
• D. 40 C

Answer 1

Answer: (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 $q=\int Idt=1.2\int tdt+3\int dt$
$q=1.2{\left[\frac{t^2}{2}\right]}_0^5+3[t{]}_0^5$
$q=\frac{1.2}{2}\times 25+3\times 5$
$q=15+15=30C$