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

Write the expression for the frequency of oscillation of an $LC$ circuit.

$A$ 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 $\phi$. At time $t=0$,the magnetic field is abruptly switched $OFF$. Let $\omega_{0}=1 / \sqrt{L C}$ and ignore the resistance of the circuit. Then,

The natural frequency of an $L-C$ circuit is $1,25,000 \text{ cycle/s}$. Then the capacitor $C$ is replaced by another capacitor with a dielectric medium of dielectric constant $K$. In this case,the frequency decreases by $25 \text{ kHz}$. The value of $K$ is

An $LC$ circuit contains a $20 \; mH$ inductor and a $50 \; \mu F$ capacitor with an initial charge of $10 \; mC$. The resistance of the circuit is negligible. Let the instant the circuit is closed be $t=0$.
$(a)$ What is the total energy stored initially? Is it conserved during $LC$ oscillations?
$(b)$ What is the natural frequency of the circuit?
$(c)$ At what time is the energy stored $(i)$ completely electrical (i.e.,stored in the capacitor)? $(ii)$ completely magnetic (i.e.,stored in the inductor)?
$(d)$ At what times is the total energy shared equally between the inductor and the capacitor?
$(e)$ If a resistor is inserted in the circuit,how much energy is eventually dissipated as heat?

$A$ $60\,\mu F$ capacitor is charged to $50\, V$. This charged capacitor is connected across a $1.5\, mH$ coil,so that $LC$ oscillations occur. The max current in the coil is......$A$