LC Oscillations

The current through a coil of self-inductance L=2mH is given by $i=t^2{e}^{-t}$ at time t. How long it will take to make the emf zero?

When current in coil changes from $5 \mathrm{A}$ to $2 \mathrm{A}$ in $0.1 \mathrm{s}$, an average of $50 \mathrm{V}$ is produced. The self-inductance in $\mathrm{Henry}\left(\mathrm{H}\right)$ of the coil is $\frac{n}{3}$. Write the value of $n$.

What is LC oscillation?

A circuit consists of a coil with inductance $L$ and an uncharged capacitor of capacitance $C$. The coil is in a constant uniform magnetic field such that the flux through the coil is $\varphi$. At time $t=0 \min$, the magnetic field is abruptly switched OFF. Let ${\omega }_0=\frac{1}{\sqrt{LC}}$ and ignore the resistance of the circuit. Then,

A $60\mu \mathrm{F}$ capacitor is charged to $100 \mathrm{volts}$. This charged capacitor is connected across a $1.5\mathrm{mH}$ coil, so that $\mathrm{LC}$ oscillations occur. The maximum current in the coil is:-

In an $LC$ circuit shown in figure, $C=2 \mathrm{F}$ and $L=2 \mathrm{H}$. At time $t=0$, charge on the capacitor is $3$ coulomb and it is decreasing with rate of $\sqrt{4} \mathrm{C} {\mathrm{s}}^{-1}$. Then choose the correct statement.

For the circuit shown in the figure, the current through the inductor is $0.6 \mathrm{A}$, while the current through the capacitor is $0.4 \mathrm{A}$. The current drawn from the generator is:

The natural frequency of the circuit is (in $\mathrm{rad} {\mathrm{s}}^{-1}$),

In an LC oscillator circuit L = 10 mH, C = 40µF. If initially at t = 0 the capacitor is fully charged with 4µC then find the current in the circuit when the capacitor and inductor share equal energies. 

The diagram shows a capacitor C and a resistor R connected in series to an AC source, V₁ and V₂ are voltmeters and A is an ammeter. Consider now the following statements :

(I) Readings in A and V₁ are always in phase

(II) Readings in A and V₂ are always in phase

(III) Reading in V₁ is ahead with reading in V₂

Which of these statements are is correct : 

The switch in the circuit pictured is in position a for a long time. At t = 0 the switch is moved from a to b. The current through the inductor will reach its first maximum after moving the switch in a time : -

Initially, the key was placed on $\left(1\right)$ till the capacitor got fully charged. Now the key is placed on $\left(2\right)$ at $t=0$. The minimum time when the energy in both capacitor and inductor will be the same.

A charged $30 \mathrm{\mu }\mathrm{F}$ capacitor is connected to a $27 \mathrm{m}\mathrm{H}$ inductor. The angular frequency of free oscillations of the circuit is

How oscillations are produced using inductor and capacitor?

A $1.5\mu \mathrm{F}$ capacitor is charged to $60\mathrm{V}$ and a$15\mathrm{mH}$ coil is connected across it. Assuming that the circuit contains no resistance, what will be the maximum current in the coil?

An inductor and two capacitors are connected in the circuit as shown in figure. Initially capacitor $\mathrm{A}$ has no charge and capacitor $\mathrm{B}$ has $\mathrm{C}\mathrm{V}$ charge. Assume that the circuit has no resistance at all. At $\mathrm{t}=0,$ switch $\mathrm{S}$ is closed, then given $\left[ \mathrm{L}\mathrm{C}=\frac{2}{{\mathrm{\pi }}^2\times {10}^4}{\mathrm{s}}^2 \& \mathrm{C}\mathrm{V}=100 \mathrm{m}\mathrm{C}\right]$

A $1.5 \mathrm{\mu }\mathrm{F}$ capacitor is charged to $60 \mathrm{V}$. The charging battery is then disconnected and a $15 \mathrm{m}\mathrm{H}$ coil is connected in series with the capacitor so that $\mathrm{LC}$ oscillations occur. Assuming that the circuit contains no resistance, the maximum current in this coil shall be close to

An $LC$ circuit contains a $20\mathrm{ }\mathrm{m}\mathrm{H}$ inductor and a $50 \mathrm{\mu }\mathrm{F}$ capacitor with an initial charge of $10\mathrm{ }\mathrm{mC}$. The resistance of the circuit is negligible. Let the instant at which the circuit which is closed be $t=0$. At what time the energy stored is completely magnetic?

A circuit has a self inductance of $1$ henry and carries a current of $2 \mathrm{A}$. To prevent sparking when the circuit is broken, a capacitor which can withstand $400 \mathrm{volts}$ is used. The least capacitance of the capacitor connected across the switch must be equal to

The natural frequency of an LC circuit is 125 kHz. When the capacitor is totally filled with a dielectric material, the natural frequency decreases by 25 kHz. Dielectric constant of the material is nearly