LC Oscillations

The natural frequency of L-C circuit is $125000$ Hz. Then the capacitor C is replaced by another capacitor with a dielectric medium of dielectric constant K. Now the frequency decreases by $25$ KHz. The value of K is

A $40\ \mu$F capacitor is charged to $10$ volts of potential. The battery is disconnected, and a pure $100$ mH coil is connected across the capacitor so that LC oscillations are set up. Then, the maximum current in the coil is:

A $10\ \mu$F capacitor is charged to $25$ V of potential. The battery is then disconnected and a pure $100$ mH coil is connected across the capacitor so that L-C oscillations are set up. The maximum current in the coil is

In an oscillating LC circuit the maximum charge on the capacitor is Q. When the energy is stored equally between the electric and magnetic fields, the charge on the capacitor (q) is

In an oscillating LC circuit, the maximum charge on the capacitor is Q. When the energy is stored equally between the electric and magnetic fields, the charge on the capacitor becomes

A capacitor C is first charged fully with potential difference of $V_0$ and disconnected from the battery. The charged capacitor is connected across an inductor having inductance L. In $t$ s, 25% of the initial energy in the capacitor is transferred to the inductor. The value of $t$ is ________ s.

If maximum energy is stored in a capacitor at $t = 0$ then the time after which, current in the circuit will be maximum is

A $1\,\mu\text{F}$ capacitor is charged to 50 V and is then discharged through 10 mH inductor of negligible resistance. The maximum current in the inductor is

In the given circuit, when $S_1$ is closed, the capacitor gets fully charged. Now $S_1$ is open and $S_2$ is closed. Then

A capacitor of capacitance $100\,\mu\text{F}$ is charged to a potential of $12\text{ V}$ and connected to a $6.4\text{ mH}$ inductor to produce oscillations. The maximum current in the circuit would be:

The amplitude of the charge oscillating in a circuit decreases exponentially as $Q = Q_0 e^{-Rt/2L}$, where $Q_0$ is the charge at $t = 0\text{ s}$. The time at which charge amplitude decreases to $0.50Q_0$ is nearly: [Given that $R = 1.5\,\Omega,\ L = 12\text{ mH},\ \ln(2) = 0.693$]

In an LC oscillator, if values of inductance and capacitance become twice and eight times, respectively, then the resonant frequency of oscillator becomes $x$ times its initial resonant frequency $\omega_0$. The value of $x$ is:

An oscillating LC circuit consists of a $75\text{ mH}$ inductor and a $1.2\,\mu\text{F}$ capacitor. If the maximum charge to the capacitor is $2.7\,\mu\text{C}$. The maximum current in the circuit will be ___________ $\text{mA}$

In an oscillating LC circuit, the maximum charge on the capacitor is '$Q$'. When the energy is stored equally between the electric and magnetic fields, the charge on the capacitor becomes

A capacitor of capacitance 500 $\mu$F is charged completely using a dc supply of 100 V. It is now connected to an inductor of inductance 50 mH to form an LC circuit. The maximum current in LC circuit will be _______ A.

The frequency of the output signal of an LC oscillator circuit is '$F$' Hz with a capacitance of 0.1 $\mu\text{F}$. If the value of the capacitor is increased to $0.2\ \mu\text{F}$, then the frequency of the output signal will be

A capacitor of capacity '$C$' is charged to a potential '$V$'. It is connected in parallel to an inductor of inductance '$L$'. The maximum current that will flow in the circuit is

A LCR circuit behaves like a damped harmonic oscillator. Comparing it with a physical spring-mass damped oscillator having damping constant 'b', the correct equivalence would be:

An ideal capacitor of capacitance $0.2\,\mu F$ is charged to a potential difference of $10\ V.$ The charging battery is then disconnected. The capacitor is then connected to an ideal inductor of self inductance $0.5\ mH.$ The current at a time when the potential difference across the capacitor is $5\ V,$ is:

An $LCR$ circuit is equivalent to a damped pendulum. In an $LCR$ circuit the capacitor is charged to $Q_0$ and then connected to the $L$ and $R$ as shown below:

If a student plots graphs of the square of maximum charge $\left(Q_{Max}^2\right)$ on the capacitor with time$(t)$ for two different values $L_1$ and $L_2\ (L_1 > L_2)$ of $L$ then which of the following represents this graph correctly?

(plots are schematic and not drawn to scale)

In a series L - C - R circuit, $C = 10^{-11}$ Farad, $L = 10^{-5}$ Henry and $R = 100$ Ohm, when a constant D.C. voltage E is applied to the circuit, the capacitor acquires a charge $10^{-9}$ C. The D.C. source is replaced by a sinusoidal voltage source in which the peak voltage $E_0$ is equal to the constant D.C. voltage E. At resonance the peak value of the charge acquired by the capacitor will be:

A fully charged capacitor $C$ with initial charge $q_0$ is connected to a coil of self inductance $L$ at $t = 0.$ The time at which the energy is stored equally between the electric and the magnetic fields is:

A condenser of capacity C is charged to a potential difference of V1. The plates of th condenser are then connected to an ideal inductor of inductance L. The current through the inductor when the potential difference across the condenser reduces to V2 is

A transistor-oscillator using a resonant circuit with an inductor L (of negligible resistance) and a capacitor C in series produce oscillations of frequency $f$. If L is doubled and C is changed to 4C, the frequency will be

In an oscillating $LC$ circuit the maximum charge on the capacitor is $Q$. The charge on the capacitor when the energy is stored equally between the electric and magnetic field is