Q 1 :

A capacitor of capacitance 100 $\mu F$ is charged to a potential of 12 V and connected to a 6.4 mH inductor to produce oscillations. The maximum current in the circuit would be                     [2024]

• 3.2 A

   

• 1.5 A

   

• 2.0 A

   

• 1.2 A

   

Q 2 :

In an LC oscillator, if values of inductance and capacitance become twice and eight times, respectively, then the resonant frequency of the oscillator becomes $\text{'}x\text{'}$ times its initial resonance frequency ${\omega }_0$. The value of $\text{'}x\text{'}$ is                      [2023]

• $\frac{1}{4}$

   

• $4$

   

• $16$

   

• $\frac{1}{16}$

   

Q 3 :

An oscillating LC circuit consists of a 75 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 ______ mA.                        [2023]

Q 4 :

A coil has an inductance of 2 H and resistance of $4\Omega$. A 10 V is applied across the coil. The energy stored in the magnetic field after the current has built up to its equilibrium value will be _________ $\times {10}^{-2}\text{\hspace{0.05em}J}$.                          [2023]

Q 5 :

Inductance of a coil with ${10}^4$ turns is 10 mH and it is connected to a dc source of 10 V with internal resistance of $10\Omega$. The energy density in the inductor when the current reaches $\left(\frac{1}{e}\right)$ of its maximum value is $\alpha \pi \times \frac{1}{e^2}{\text{J/m}}^3$. The value of $\alpha$ is ________.       $({\mu }_0=4\pi \times {10}^{-7}\text{Tm/A})$ .                             [2026]