Question

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

Answer 1

(a) for discharging circuit
$i=i_0{e}^{-t/\tau }\Rightarrow 1=2e^{-0.1/\tau }\Rightarrow \left(1/2\right)=e^{-0.1/\tau }\Rightarrow ln\left(1/2\right)=\ln \left(e^{-0.1/\tau }\right)\Rightarrow \tau =0.1/0.693=0.144=0.14$
(b) $L=4H,i=L/R$
$\Rightarrow$ $0.14=4R$
$\Rightarrow$ $R=4/0.14=28.57=28\Omega$