LC oscillations

Consider a circuit consisting of a capacitor of capacitance $C$ and a coil with $N$ turns per unit length, cross sectional area $S$ and length $d$, where $d^2\gg S$. There is another coil of length $d/2$, cross sectional area $S/2$ and $2N$ turns per unit length completely inside the larger coil, as shown in the figure. The ends of this smaller coil are connected with each other by an insulated conducting wire. The self-inductance of the larger coil is $L$. Neglecting edge effects and all the Ohmic resistances, the resonant frequency of the circuit is:

The circuit shown in the figure contains an inductor $L$, a capacitor $C_0$, a resistor $R_0$ and an ideal battery. The circuit also contains two keys K₁ and K₂. Initially, both the keys are open and there is no charge on the capacitor. At an instant, key K₁ is closed and immediately after this the current in $R_0$ is found to be $I_1$. After a long time, the current attains a steady state value $I_2$. Thereafter, K₂ is closed and simultaneously K₁ is opened and the voltage across $C_0$ oscillates with amplitude $V_0$ and angular frequency $\omega_0$.

Match the quantities mentioned in List-I with their values in List-II and choose the correct option.

Consider an LC circuit, with inductance $L = 0.1$ H and capacitance $C = 10^{-3}$ F, kept on a plane. The area of the circuit is $1\ \mathrm m^2$. It is placed in a constant magnetic field of strength $B_0$ which is perpendicular to the plane of the circuit. At time $t = 0$, the magnetic field strength starts increasing linearly as $B = B_0 + \beta t$ with $\beta = 0.04\ \mathrm{T\,s^{-1}}$. The maximum magnitude of the current in the circuit is _____ mA.

If L, C and R are the self inductance, capacitance and resistance respectively, which of the following does not have the dimension of time?

A capacitor of capacitance 500 μF 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.