The time constant of inductance coil is 3 ms. When a 90 `omega` resistance is joined in series, then the time constant becomes 0.5 ms. The inductance and the resistance of the coil are

Options

A. 54 mH , 18`omega`
B. 14 mH , 42`omega`
C. 42 mH , 14`omega`
D. 14 mH , 60`omega`

Answer

(a)

Explanation

Time constant ,
`t = L/R`
`3 = L/R` …..(1)
When a 90 `omega` resistance is connected in series , the time constant become 0.5 ms
`rArr 0.5 = L/R + 90` …..(2)
From equation (1) and (2), we get
`rArr 30/5 = R + 90/R`
`rArr 5R = 90`
`:. R = 18 omega`
On substituting the value of R in equation (1) ,we get
`3 xx 10^(-3) = L/18`
`rArr L = 54 mH`