A coil of some internal resistance `'r'` behaves line an inductance. When it is connected in series with a resistance `R_(1)`, the time constant is found to be `tau_(1)`. When it is connected in series with a resistance `R_(2)`, the time constant is found to be `tau_(2)`. The inductance of the coil is

Options

A. `(tau_(1)tau_(2)(R_(1)-R_(2)))/((tau_(2)-tau_(1)))`
B. `((tau_(2)-tau_(1)))/(tau_(1)tau_(2)(R_(1)-R_(2)))`
C. `((R_(1)-R_(2)))/((tau_(2)-tau_(1)))`
D. `((tau_(2)-tau_(1)))/((R_(1)-R_(2)))`

Answer

A

Explanation

`tau_(1) = (L)/(R_(1)+r) , tau_(2) = (L)/(R_(2) + r)`