LR Circuit with DC Source

A coil having inductance $L$ and resistance $R$ is connected to a battery of emf $\epsilon$ at $t=0$. If $t_1$ and $t_2$ are the time for $90\%$and $99\%$completion of the current growth in the circuit, then $\frac{t_2}{t_1}$ will be-

The time constant of the given circuit, containing an inductor and few resistors, is 

In the circuit shown here, the point '$C$' $A$is kept connected to point '' till the current flowing through the circuit becomes constant. Afterwards, suddenly, point '$C$' $A$is disconnected from point '' and connected to point '$B$' at time $t=0$. Ratio of the voltage across resistance and the inductor at $t=\frac{L}{R}$ will be equal to:

          

In the given circuit $S_1$and $S_2$ are switches. $S_2$ is closed for a long time and $S_1$ remains open. Now $S_1$ is also closed. Here $R=10 \Omega ,L=1 \mathrm{mH}$ and $\epsilon =3 \mathrm{V}$. Let $\frac{\mathrm{di}}{\mathrm{dt}}$ is the magnitude of rate of change of current (in $\mathrm{A} {\mathrm{s}}^{-1}$), just after $S_1$ is closed. The value for the inductor $L$ is $\frac{\mathrm{d}i}{\mathrm{d}t}=x\times {10}^3 \mathrm{A} {\mathrm{s}}^{-1}$. Then find $x$.

In the figure shown the battery is ideal. The values are $\epsilon =10 \mathrm{V}, R=5 \mathrm{\Omega },\mathit{ }L=2 \mathrm{H}$. The current through the battery at $t=2 \mathrm{s}$ after closing the switch is:

When a $LR$ circuit with $L=3 \mathrm{mH}$ is connected in series to an $AC$ source of $\mathrm{rms}$ voltage $30 \mathrm{V},$ a maximum rms current of $6 \mathrm{A}$ is observed at frequency $\left(\frac{500}{\pi }\right)\mathrm{Hz}.$ If this $LR$ circuit is now connected to a battery of emf $21 \mathrm{V}$ and internal resistance of $3 \mathrm{\Omega },$ the current will be

The value of time constant for given circuit is $\dots ....s$

In the given branch $\mathrm{AB}$ of a circuit a current $\mathrm{I}=(10 \mathrm{t}+5) \mathrm{A}$ is flowing, where $\mathrm{t}$ is time in second. At $\mathrm{t}=0,$ the potential difference between points $\mathrm{A}$ and $\mathrm{B}\left({\mathrm{V}}_{\mathrm{A}}-{\mathrm{V}}_{\mathrm{B}}\right)$ is :

In the circuit shown in figure switch S is closed at time $\mathrm{t}=0$.The charge which passes through the battery in one time constant is :

In which of the following circuit is the current maximum just after the switch S is closed:

A solenoid has an inductance of $60 \mathrm{henry}$ and a resistance of $30 \mathrm{ohm}$. If it connected to a $100 \mathrm{volt}$ battery, how long will it take for the current to reach $\frac{e-1}{e}\approx 63.2\%$ of its final value?

Two resistance $20\mathrm{\Omega }$ and $50\mathrm{\Omega }$ and a pure inductance of $50 \mathrm{H}$ are connected to a $10 \mathrm{V}$ battery through a key as shown in the figure. The key is tapped at $t=0$. Find the final value of current in the $50\mathrm{\Omega }$ resistor :

An $LR$ circuit having $L=4 \mathrm{H}, R=1 \mathrm{\Omega }$ and $E=6 \mathrm{V}$ is switched on at $t=0.$ The power dissipated in joule heating at $t=4 \mathrm{s}$ is

A metallic core made of paramagnetic substance $\left({\mu }_r=2\right)$ and of same size as that of the air core solenoid (self induction $L$) is inserted suddenly $\left(t=0\right)$ within the space of the core solenoid as shown in the figure. (ignore resistance of the solenoid as well as the end effects) and assume solenoid is of infinite length. Identify the correct option. Assume that charge flowing to the circuit is negligible.

When an inductor coil carrying a steady current is short-circuited, the current in it becomes $\beta (<1)$ times its initial value in a time $T$. The time constant of the choke coil is:

In the circuit shown in the figure switch $\mathrm{S}$ is closed at $t=0$. Then which of the following statements is WRONG.

$\left(\mathrm{Given} : R=\sqrt{\frac{L}{2C}}\right)$

In the $\mathrm{LR}$ circuit as shown in figure, the switch is closed at $t=0$. Mark the incorrect statement of the following:

The time constant of a circuit is $10 \sec$, when a resistance of $10 \mathrm{\Omega }$ is connected in series in a previous circuit then time constant becomes $2$ second, then the self inductance of the circuit is:-

In the inductive circuit given in the figure, the current rises after the switch is put on. At instant when the current is $15 \mathrm{mA},$ then potential difference across the inductor will be :-

$\mathrm{A}$coil of inductance $300 \mathrm{mH}$ and resistance $2 \mathrm{\Omega }$  is connected to a source of voltage $2 \mathrm{V}$. The current reaches half of its steady value in :-