Question

If the current through a 0.1 H inductor is $i\left(t\right)=10t{e}^{-5t}A,$ then the energy stored at t=1 sec is

• A. $91\times {10}^{-6}J$
• B. $333\times {10}^{-6}J$
• C. $500\times {10}^{-6}J$
• D. $277\times {10}^{-6}J$

Answer 1

The correct option is D $277\times {10}^{-6}J$

$i\left(t\right)=10t{e}^{-5t}A,$
Energy stored, $E=\frac{1}{2}L{i}^2=\frac{1}{2}\times 0.1\times (10t{e}^{-5t}{)}^2$
$\frac{0.1}{2}\times 100t^2{e}^{-10t}=5t^2{e}^{-10t}$
At t = 1 sec, $E_{1sec}=5\times 1\times e^{-10}$
$=\frac{5}{e^{10}}=227\times {10}^{-}6=227\mu J$