The time constant of an $LR$ circuit represents the time in which the current in the circuit

An inductor with an iron core is connected in series with a resistor $R$ across an ideal $DC$ source. The circuit is in a steady state. If the iron core is removed, what happens to the current flowing through the inductor immediately after the removal of the core?

The current $(i)$ at time $t = 0$ and $t = \infty$ respectively for the given circuit is

For $L-R$ circuit,the time constant is equal to

Switch $S$ of the circuit shown in the figure is closed at $t = 0$. If $e$ denotes the induced $emf$ in $L$ and $i$ the current flowing through the circuit at time $t$,which of the following graphs is correct?

In the circuit shown, when the current $i$ is $3 \text{ A}$ and increasing at the rate of $1 \text{ A/s}$, the potential difference between $A$ and $B$ is $12 \text{ V}$. When the same current $3 \text{ A}$ is decreasing at the rate of $1 \text{ A/s}$, the potential difference between $A$ and $B$ is $6 \text{ V}$. The value of $R$ in the circuit is: (in $\text{ } \Omega$)