Question

After how much time energy becomes $\frac{1}{e}$ of the maximum value in a $R-L$ circuit where $R=2\Omega$ and $L=2\text{mH}$, if the energy at t=0 is maximum?

• A. $1\text{ms}$
• B. $0.5\text{ms}$
• C. $2\text{ms}$
• D. $1.5\text{ms}$

Answer 1

The correct option is B $0.5\text{ms}$

$U=U_0{\left[e^{-t/\tau }\right]}^2$
$\frac{U_0}{e}=U_0{\left[e^{-t/\tau }\right]}^2$
$\Rightarrow e^{-1/2}=e^{-t/\tau }\Rightarrow \frac{t}{\tau }=\frac{1}{2}$
$\Rightarrow t=\frac{\tau }{2}=\frac{\left(L/R\right)}{2}=\frac{2\times {10}^{-3}}{2\times 2}=0.5\text{ms}$