Class 12th

Ore                                                   Formula

Siderite                                            FeCO₃

Malachite                                        CuCO₃ Cu (OH)₂

Calamine                                         ZnCO₃

Sphalarite                                       ZnS

Decay of current in Inductor is given by,

              $i=i_0{e}^{-t/\tau }\left[Where\tau =\raisebox{1ex}{$L$}\!\left/ \!\raisebox{-1ex}{$R$}\right.;i_0=\frac{v}{R}=\frac{20}{10}=2\right]$  

              At t = 100 $\mu s$  

              i = 0

              i.e. i = i₀ $e^{-100/\tau }=0$           -(1)

              e.m.f   induced

              $e=\frac{-Ldi}{dt}=-L\frac{d}{dt}\left[i_0{e}^{-t/\tau }\right]$  

              = $=-L{i}_0\frac{-1}{2}{e}^{-t/\tau }$

              $e=\frac{L{i}_0}{\tau }{e}^{-t/\tau }$

$e_{avg}=\frac{{\displaystyle \underset{0}{\overset{200\mu s}{\int }}edt}}{{\displaystyle \underset{0}{\overset{200\mu s}{\int }}dt}}=\frac{{\displaystyle \underset{0}{\overset{200\mu s}{\int }}\frac{L{i}_0}{\tau }{e}^{-t/\tau }dt}}{{\displaystyle \underset{0}{\overset{200\mu s}{\int }}dt}}$

$=\frac{L{i}_0}{200*10^{-6}sec}=\frac{20*10^{-3}*2}{200*10^{-6}}=400$