Question

Determine the energy stored in the inductor L as a function of time for the LR circuit of the figure. Express your answer in terms of the variables L, t, R, V_0, and appropriate constants. U = After how many time constants does the stored energy reach 99.9% of its maximum value? Express your answer using two significant figures. t =

Answer 1

Current in LR circuit is given by

$I(t)=\frac{V_o}{R}(1-e^{-Rt/L})$

(a) Energy stored in the inductor is given by

$E=\frac{1}{2}. L. I(t)^2$

$\Rightarrow E(t)=\frac{LV_o^2}{2R^2}(1-e^{-Rt/L})^2$

(b) According to question, we need to find time for which

$\frac{99.9}{100}\times \frac{LV_o^2}{2R^2} =\frac{LV_o^2}{2R^2}(1-e^{-t/\tau})^2$

$\Rightarrow\ \ \ t \approx 7.60\tau$

Hope this helps.