At t=0, an inductor of zero resistance is joined to a cell of emf `epsilon` through a resistance. The current increases with a time constant `tau`. After what time will the potential difference across the coil be equal to that across the resistance ?

Explanation

`V_L = V_R`
`E^((Rt)/(L)) = E (1- e^((Rt)/(L)))`
` rArr 2e^(-(Rt)/(L)) = 1 , e^(-R/L t) = 1/2 , e^(R/L t) = 2`
` (Rt)/(L) = ln 2(or ) t = L/R ln 2`