LC Oscillations

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

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

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 $\left[ \mathrm{L}\mathrm{C}=\frac{2}{{\mathrm{\pi }}^2\times {10}^4}{\mathrm{s}}^2 \& \mathrm{C}\mathrm{V}=100 \mathrm{m}\mathrm{C}\right]$

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

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

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

The capacitance in an oscillatory LC circuit is increased by $1\%$. The change in inductance required to restore its frequency of oscillation is to

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

In AC circuit in which inductance and capacitance are joined in series. Current is found to be maximum when the value of inductance is $0.5 \mathrm{H}$ and the value of capacitance is $8\mathrm{ }\mu \mathrm{F}$. The angular frequency of applied alternating voltage will be

A circuit consists of an inductance of $0.5 \mathrm{mH}$ and a capacitor of $20 \text{μF}$. The frequency of the $LC$ oscillations is approximately

In a series resonant R-L-C circuit, the voltage across R is 100 V and the value of $=1000 \mathrm{\Omega }$ . The capacitance of the capacitor is $2\times {10}^{-6} \mathrm{F};$ angular frequency of AC is $200\mathrm{ }\mathrm{r}\mathrm{a}\mathrm{d}\mathrm{ }{\mathrm{s}}^{-1}.$ Then the potential difference across the inductance coil is

Let $L$ denote the self-inductance of coil which is in series with a capacitor of capacitance $C$. Which of the following has the unit second?

The frequency of oscillation of current in the inductor is-

The natural frequency of an LC circuit is $125000 \mathrm{cycles} {\mathrm{s}}^{-1}$. Then the capacitor $C$ is replaced by another capacitor with a dielectric medium of dielectric constant $K$. In this case, the frequency decreases by $25 \mathrm{kHz}$. The value of $K$ is

The natural frequency of an $L-C$ circuit is $125000 \mathrm{cycles}/\mathrm{s}$. When a dielectric medium of dielectric constant $K$ is introduced between the plates of the capacitor, the frequency decreases by $25 \mathrm{kHz}$. The value of $K$ is

Choose the wrong statement.