LR circuits

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

The circuit shown in the figure contains an inductor $L$, a capacitor $C_0$, a resistor $R_0$ and an ideal battery. The circuit also contains two keys K₁ and K₂. Initially, both the keys are open and there is no charge on the capacitor. At an instant, key K₁ is closed and immediately after this the current in $R_0$ is found to be $I_1$. After a long time, the current attains a steady state value $I_2$. Thereafter, K₂ is closed and simultaneously K₁ is opened and the voltage across $C_0$ oscillates with amplitude $V_0$ and angular frequency $\omega_0$.

Match the quantities mentioned in List-I with their values in List-II and choose the correct option.

For the given circuit the current through battery of 6 V just after closing the switch 'S' will be ______ A.

A coil of inductance 1 H and resistance 100 Ω is connected to a battery of 6 V. Determine approximately :

(a) The time elapsed before the current acquires half of its steady - state value.

(b) The energy stored in the magnetic field associated with the coil at an instant 15 ms after the circuit is switched on. (Given ln2 = 0.693, $e^{-3/2}$ = 0.25)

The inductors of two $LR$ circuits are placed next to each other, as shown in the figure. The values of the self-inductance of the inductors, resistances, mutual-inductance and applied voltages are specified in the given circuit. After both the switches are closed simultaneously, the total work done by the batteries against the induced $EMF$ in the inductors by the time the currents reach their steady state values is ______ mJ.

A 10 cm long perfectly conducting wire PQ is moving with a velocity 1 cm/s on a pair of horizontal rails of zero resistance. One side of the rails is connected to an inductor $L = 1$ mH and a resistance $R = 1\ \Omega$ as shown in figure. The horizontal rails, $L$ and $R$ lie in the same plane with a uniform magnetic field $B = 1$ T perpendicular to the plane. If the key S is closed at certain instant, the current in the circuit after 1 millisecond is $x\times10^{-3}$ A, where the value of $x$ is ______.

[Assume the velocity of wire PQ remains constant (1 cm/s) after key S is closed. Given: $e^{-1} = 0.37$, where $e$ is base of the natural logarithm]

In the figure below, the switches $S_1$ and $S_2$ are closed simultaneously at $t = 0$ and a current starts to flow in the circuit. Both the batteries have the same magnitude of the electromotive force (emf) and the polarities are as indicated in the figure. Ignore mutual inductance between the inductors. The current $I$ in the middle wire reaches its maximum magnitude $I_{max}$ at time $t = \tau$. Which of the following statements is (are) true?

A source of constant voltage $V$ is connected to a resistance $R$ and two ideal inductors $L_1$ and $L_2$ through a switch $S$ as shown. There is no mutual inductance between the two inductors. The switch $S$ is initially open. At $t = 0$, the switch is closed and current begins to flow. Which of the following options is/are correct?

Two inductors $L_1$ (inductance 1 mH, internal resistance 3 Ω) and $L_2$ (inductance 2 mH, internal resistance 4 Ω), and a resistor $R$ (resistance 12 Ω) are all connected in parallel across a 5 V battery. The circuit is switched on at time $t=0$. The ratio of the maximum to the minimum current $(I_{\max}/I_{\min})$ drawn from the battery is

A series LR circuit is connected to a voltage source with $V(t)=V_0\sin\Omega t$. After very large time, current I(t) behaves as $\left(t_0>>\dfrac LR\right)$ :

An inductor (L = 0.03H) and a resistor (R = 0.15 kΩ) are connected in series to a battery of 15V EMF in a circuit shown below. The key $K_1$ has been kept closed for a long time. Then at t = 0, $K_1$ is opened and key $K_2$ is closed simultaneously. At t = 1ms, the current in the circuit will be : ($e^5\cong150$)

In the circuits (a) and (b) switches $S_1$ and $S_2$ are closed at t = 0 and are kept closed for a long time. The variation of currents in the two circuits for t ≥ 0 are roughly shown by (figures are schematic and not drawn to scale) :

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