Question

a coil of resistance 50 ohm and inductance 80H connected to 200 V battery. The time in which the current is 50% of its peak value

Answer 1

you know the l-r equation?

one formulation as follows:
\[I(t) = \frac{V_{o}}{R} ( 1- e^\frac{-tR}{L})\]

you are trying to find time T when I(T) = 50% V/R, V/R being the peak value of current when the inductor has stopped resisting the current of the battery.

so you need to solve this:
\[1- e^\frac{-tR}{L} = 0.5\]

ie
\[e^\frac{-tR}{L} = 0.5\]

Answer 2

Thank You...

Answer 3

Determine the peak current. This can be found by as pointed by IrishBoy123, the peak current will be when for all practical purposes the "counter electromotive force" is negligible and the only opposition is by the resistance of 50 Ohms, that would be 4 amps 50% of that would be 2 amps. So plug 2 in I(t) position of the First formula provided by IrishBoy123 and solve for t.

Answer 4

Actually IrishBoy123 method is better, I just wanted to emphasize how the 50% peak current was obtained.