In the figure shown `i=10e^(-4t)`A. Find `V_L` and `V_(ab)`

Explanation

Potential difference across the inductor is given as
`V_(L)=+L(di)/(dt)=(2)(d)/(dt)(10e^(-4t))=-80e^(-4t)`
Further, by using Kirchhoff's second law,
`V_(a)-iR-L(di)/(dt)=V_(b)`
`thereforeV_(a)-V_(b)=iR+L(di)/(dt)" or "V_(ab)=(10e^(-4t))(4)-80e^(-4t)=-40e^(-4_(t))`