The figure shows an $L-R$ circuit. When the switch $S$ is closed,the currents through resistors $R_1, R_2$ and $R_3$ are $I_1, I_2$ and $I_3$ respectively. The values of $I_1, I_2$ and $I_3$ at $t=0 \, s$ are:

Consider an electrical circuit containing a two-way switch $S$. Initially,$S$ is open and then $T_{1}$ is connected to $T_{2}$. As the current in $R = 6 \, \Omega$ attains a maximum value of steady-state level,$T_{1}$ is disconnected from $T_{2}$ and immediately connected to $T_{3}$. The potential drop across the $r = 3 \, \Omega$ resistor immediately after $T_{1}$ is connected to $T_{3}$ is $.... \, V$. (Round off to the nearest integer)

An inductor $(L)$ - resistance $(R)$ battery circuit is switched on at $t = 0$. If the $e.m.f.$ of the battery is $E$,what is the charge passing through the battery in time constant $T$?

Two resistors of $10\, \Omega$ and $20\, \Omega$ and an ideal inductor of $10\, H$ are connected to a $2\, V$ battery as shown. The key $K$ is inserted at time $t = 0$. The initial $(t = 0)$ and final $(t \rightarrow \infty)$ currents through the battery are

An inductor of inductance $10 \text{ mH}$ having resistance of $100 \ \Omega$ is connected to a battery of $E$.$M$.$F$. $1.0 \text{ V}$ through a switch as shown in the figure below. After the switch is closed, the ratio of instantaneous voltages across the inductor when the current passing through it is $2 \text{ mA}$ and $4 \text{ mA}$ is . . . . . . .

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 $\text{ } \Omega$)