Question

The potential difference across a 2H inductor as a function of time is shown in the figure. At time t = 0, current is zero. Choose the correct statement

• A. Current at t = 2 sec is 5A
• B. Current at t = 2 sec is 10 A
• C. Current vs time graph across inductor will be
  
• D. Current vs time graph across inductor will be
  

Answer 1

Answer: (A), (C)

The correct options are
A Current at t = 2 sec is 5A
C Current vs time graph across inductor will be


Area in $(V_L-t)graph=L\Delta I$
$\Rightarrow 2(i_f-0)=\frac{1}{2}\times 10\times 2\Rightarrow i_f=5A\int di=\frac{1}{L}\int V_L.dtFromt=0tot=2sec;V_L=5t\Rightarrow i=\frac{1}{L}\left[\frac{5}{2}{t}^2\right]Fromt=2tot=4sec:V_L=-5t+C\Rightarrow i=\frac{1}{L}[\frac{-5t^2}{2}+ct]$