A coil of self inductance 10 m H and resistance of 0.1 Ω is connected through a switch to a battery of internal resistance 0.9 Ω . After the switch is closed, the time taken for the current to attain 80 % of the saturation value is: [ ln 5 = 1.6 ]

Step-by-step solution

The instantaneous current in an LR circuit is given by the equation : (instantaneous current) I = I s 1 - e - R t L Where I ,   I s ,   R ,   t ,   L are the instantaneous current, saturation current, resistance, time and inductance respectively. Given that the current becomes so percent of saturation current. ⇒ 0.8   I s = I s 1 - e - R t L R = 0 . 1 Ω + 0 . 9 Ω = 1 Ω ⇒ 0.8 = 1 - e - 1 × t 10 × 10 - 3 ⇒ 0.8 = 1 - e - 100 t   Therefore, the ti