An inductor (L = 0.03 H) and a resistor (R = 0.15 `kOmega`) are connected in series to a battery of 15 V EMF in a circuit shown below The key `K_1` has been kept closed for a long time. Then at t = 0, `K_1` is opened and key `K_2` is closed simultaneously. At t = 1 ms, the current in the circuit will be : `(e^5 cong 150)`

Options

A. 100 mA
B. 67 mA
C. 6.7 mA
D. 0.67 mA

Answer

D

Explanation

`I=I_0 e^(-(RT)/L)`
`=epsilon/R e^(-(RT)/L)`
`=15/150e^(-(150xx10^(-3))/0.03)`
`=1/10 xx e^(-5)`
`=1/10xx 1/e^5`
`=1/10 xx 1/150`
`=1/1500`= 0.00067 A
`therefore` I=0.67 mA