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 $n$.

A capacitor of capacity $2\mathrm{\mu F}$ is charged to a potential difference of $12 \mathrm{V}.$ It is then connected across an inductor of inductance $0.6\mathrm{mH}.$ What is the current (in $\mathrm{mA}$) in the circuit at a time when the potential difference across the capacitor is $6.0 \mathrm{V}?$

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,

The resonance frequency of $LC$ circuit is

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 the $\mathrm{AC}$ network shown in figure, the $\mathrm{rms}$ current flowing through the inductor and capacitor are $0.6 \mathrm{A}$ and $0.8 \mathrm{A}$ respectively. Then the current coming out of the source is

A $60 \mathrm{\mu F}$ capacitor is charged to $100$ volts. This charged capacitor is connected across a $15 \mathrm{mH}$ coil, So that $\mathrm{LC}$ oscillations occur. Maximum current in the coil is :

A fully charged capacitor C with initial charge q₀ is connected to a coil of self inductances L at $\mathrm{t} = 0.$The time at which the energy is stored equally between the electric and the magnetic fields 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.

Two capacitors of capacitance $C_1$ and $C_2$ are charged to a potential difference of $V_1$ and $V_2$ respectively and are connected to an inductor of inductance $L$ as shown in the figure. Initially key $k$ is open. Now key $k$ is closed and current in the circuit starts increasing. When current in the circuit is maximum

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:

In following $L-C$ circuit at $t=0,$ charge on capacitor $q_{\max }=200\mu \mathrm{C},$ what is $\left|\frac{dI}{dt}\right|$ when $q=100 \mu \mathrm{C}$

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

In series $\mathrm{LCR}$ resonant circuit if both $L$ and $C$ are increased by $20\%$ then new resonant frequency:-

An $\mathrm{LC}$ current contains inductance $L=1 \mu \mathrm{H}$ and capacitance $C=0.01 \mu \mathrm{F}$. The wavelength of electromagnetic wave generated is nearly :-

The resonant frequency of the $L-C$ circuit is $f_0$ before insertion of the dielectric of ${\epsilon }_r=16.$ After inserting the dielectric, the resonant frequency will be :-

In an $L$-$C$ circuit which of the following is true at $t=\frac{3T}{4}$($T$ is the time period of oscillation)? Assume that at $t=0$ the capacitor is fully charged and the current in the circuit is zero.

The inductor in a $L-C$ oscillation has a maximum potential difference of $16 \mathrm{V}$ and maximum energy of $640\text{ μJ}$. find The value of capacitance in $L-C$ circuit .