Question

Consider the $LR$ circuit shown in the figure. If the switch $S$ is closed at $t = 0$ then the amount of charge that passes through the battery between $t = 0$ and $t = \frac{L}{R}$ is:

• A. $\frac{EL}{7.3 R^2}$
• B. $\frac{EL}{2.7 R^2}$
• C. $\frac{7.3 EL}{ R^2}$
• D. $\frac{2.7 EL}{ R^2}$

Answer 1

Answer: (B)

$\frac{EL}{2.7 R^2}$

Answer 2

$q = \int I dt$
$q = \int_0^{L/R} \, \frac{E}{R} \bigg[ 1 - e^{\frac{-Rt}{L}}\bigg]dt$
$q = \frac{EL}{R^2} \, \frac{1}{e}$
$q = \frac{EL}{2.7 R^2}$