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 $x$.

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

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 :-

$L\text{,} C \text{and} R$, respectively, indicate inductance, capacitance and resistance. Select the combination which does not have dimensions of frequency.

Identify the correct statement out of the following options regarding the given circuit.

For a certain inductive coil, it is known that its time constant is $2.0\times {10}^{-3} \mathrm{s}$. If a $90 \mathrm{\Omega }$ resistance is joined in series with the coil, the time constant becomes $0.5\times {10}^{-3} \mathrm{s}$. Hence, find the inductance and resistance of the coil.

With respect to the given L-R circuit, $i_1$ is the initial current and $i_2$ is the steady state current through the battery. Then, calculate the ratio $\frac{i_1}{i_2}$.

In a $\mathrm{LR}$ circuit, an inductance of $300 \mathrm{mH}$ and a resistance of $2 \mathrm{\Omega }$ are connected in series to a source of voltage $2 \mathrm{V}$. What is the time when the current in the circuit reaches half of its steady state value?

Calculate the time constant for the adjoining circuit that contains an inductor with a few resistors.

How much time does a $10 \mathrm{H}$ solenoid of $2 \mathrm{\Omega }$ resistance require, to attain the magnetic energy equal to ${\left(\frac{1}{4}\right)}^{\mathrm{th}}$ of its maximum magnetic energy, when connected to a $10 \mathrm{V}$ battery?

In the circuit shown in the figure, the switch was kept in $\mathrm{position}-1$ for a very long time and then at $t=0$ it is shifted to $\mathrm{position}-2$. The current in the circuit immediately after that is $i=\frac{a}{b} \mathrm{A}$, then the value of $a+b$ is

At $t=\mathrm{0,}$ the switch is closed. Find the time after which the rate of dissipation of energy in the resistor is equal to the rate at which energy is being stored in the inductor.

In the circuit shown,



the switch $S_1$ is closed at time $t=0$ and the switch $S_2$ is kept open. At some later time $\left(t_0\right)$ , the switch $S_1$ is opened and $S_2$ is closed. The behavior of the current $I$ as a function of time ' $t$ ' is given by:

Find the current $\mathrm{i}$ in the circuit long time after closing the switch.

In the given $L-R$ circuit, the switch $S_1$ is initially closed and $S_2$ is open. At any time $t=t_0$ , the switch $S_1$ is opened and $S_2$ is closed. The current $\left(i\right)$ vs time $\left(t\right)$ graph for the entire time during which it passes through the inductor is shown in figure. Then the best suitable graph is.

For given $\mathrm{L}-\mathrm{R}$ circuit, growth of current as function of time $\mathrm{t}$ is shown in graph. Which of the following option represents value of time constant most closely for the circuit?

In the circuit shown below, all the inductors (assumed ideal) and resistors are identical. The current through the resistance on the right is $I$ after the key $K$ has been switched on for along time. The currents through the three resistors (in order, from left to right) immediately after the key is switched off are-