The value of time constant for the given circuit is

Options

A. `(L)/(R_(1)+r+R_(2))`
B. `(L)/((R_(1)+r))`
C. `(L(R_(1)+R_(2)+r))/((R_(1)+r)R_(2))`
D. None of these

Answer

C

Explanation

After short-circuiting the battery.

Resistance, `R_(ab)=(R_(2)(R_(1)+r))/(R_(2)+R_(1)+r)`
`therefore` Time constant, `tau_(L)=(L)/(R_("net"))=(L(R_(1)+R_(2)+r))/((R_(1)+r)R_(2))`