LC Oscillations

A circuit consists of a coil with inductance $L$$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 $t=0$, the magnetic field was abruptly switched off. Let ${\omega }_0=1/\sqrt{LC}$ and ignore the resistance of the circuit. Then,

Why is self induction called inertia of electricity?

The self inductance of a long solenoid cannot be increased by

(a) increasing its area of cross section

(b) increasing its length

(c) changing the medium with greater permeability

(d) increasing the number of turns in it

(e) increasing the current through it

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 $60\mu \mathrm{F}$ 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.

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 : -

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

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

At a moment $\left(t=0\right),$ when the charge on capacitor $C_1$ is zero, the switch is closed. If $I_0$ be the current through the inductor at $t=0$, for $\mathrm{ }t>0$ (initially, $C_2\mathrm{ }$is uncharged.)

The tuning circuit of a radio receiver has a resistance of $50 \mathrm{\Omega }$, an inductor of $10\mathrm{ }\mathrm{m}\mathrm{H}$ and a variable capacitor. $1\mathrm{ }\mathrm{M}\mathrm{H}\mathrm{z}$ radio wave produces a potential difference of $0.1\mathrm{ }\mathrm{m}\mathrm{V}$. The values of the capacitor to produce resonance is (Take ${\mathrm{\pi }}^2=10$)

An oscillator circuit consists of an inductance of $0.5mH$ and a capacitor of $20\mu F$. The equivalent frequency of the circuit is nearly