The current in a discharging LR circuit without the battery drops from `2.0 A` to `1.0 A` in `0.10s` . (a) find the time constant of the circuit. (b) if the inductance of the circuit is `4.0 H`, what is its resistance?

Explanation

In a discharging circuit
`l=l_(0)e^(-t//tau)`
`l=l_(0)e^(t//tau)`
`implies 1=2e^(t//tau)`
`implies(1/2)=2e^(t//tau)`
impliesIn(1/2)=In(e^(t//tau))implies 0.653=-(0.1/(tau))`
`implies (tau)=(0.1)/(0.693)=0.144=0.14`
`(b) L=4H, (tau)=(L/R)`
implies0.14 =(4/R)`
`implies R=(4/0.14)`
`=28.5728 (Omega).`