Answer to Question #199571 in Calculus for VPM

Question #199571

1. The energy 𝑖, of an inductor with inductance 𝐿 is given by

𝑖= 12πΏβˆ«π‘‘2π‘’βˆ’π‘‘10𝑑𝑑


For 𝐿=(1 Γ—10βˆ’3)𝐻, Find 𝑖.


1
Expert's answer
2021-05-31T18:32:29-0400

Ans:-

"\\Rightarrow \ud835\udc56= 12\ud835\udc3f\\intop_0 ^1\ud835\udc61^2\ud835\udc52^{\u2212\ud835\udc61}\ud835\udc51t" where "L=1\\times 10^{-3}H"


Firstly "\\intop t^2e^{-t}= t^2(-e^{-t})-\\ \\intop-e^{-t}(2t)dt"


On Simplification


"\\Rightarrow -t^2e^{-t}+2[-te^{-t}+\\ \\intop-e^{-t}dt]\\\\\n\\Rightarrow -t^2e^{-t}\\ -2te^{-t}-2e^{-t}"


So put the value of integration in the first expression So that we can find the value of "i"


"\\Rightarrow i=12L[\u2212\nt^2e^{\u2212t}\u22122te^{\u2212t}\u22122e^{\u2212t}]_0\n ^1"


"\\Rightarrow i=12L(-5e^{-1}+2)"


"\\Rightarrow i=1.9272L"


"\\Rightarrow i =1.92\\times 10^{-3} A"


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