LC Oscillations

The natural frequency (ca₀) of oscillations in LC circuit is given by ______.

A 10 μF capacitor is charged to a 25 volt of potential. The battery is disconnected and a pure 100 m H coil is connected across the capacitor so that LC oscillations are set up. Calculate the maximum current in the coil.

A charged 10 microfarad capacitor is connected to an 81 mH inductor. What is the angular frequency of free oscillations of the circuit?  

Answer in brief.

What is the natural frequency of the LC circuit? What is the reactance of this circuit at this frequency?

A radio can tune over the frequency range of a portion of the MW broadcast band (800kHz -1200kHz). If its LC circuit has an effective inductance of 200mH, what must be the range of its variable condenser? 

A radio can tune over the frequency range of a portion of MW broadcast band: (800 kHz to 1200 kHz). If its LC circuit has an effective inductance of 200 µH, what must be the range of its variable capacitor?

[Hint: For tuning, the natural frequency i.e., the frequency of free oscillations of the LC circuit should be equal to the frequency of the radio wave.]

Calculate the quality factor of a series LCR circuit with L = 2.0 H, C = 2μF and R = 10 Ω. Mention the significance of quality factor in LCR circuit.

In a series LR circuit X_L = R and power factor of the circuit is P₁. When capacitor with capacitance C such that X_L = X_C is put in series, the power factor becomes P₂. Calculate P₁/P₂.