If the capacitance of the LC oscillation circuit is increased, then the time period of the oscillation of charge will:

CONCEPT:

LC Oscillations:

• We know that a capacitor and an inductor can store electrical and magnetic energy, respectively.
• When a capacitor (initially charged) is connected to an inductor, the charge on the capacitor and the current in the circuit exhibit the phenomenon of electrical oscillations similar to oscillations in mechanical systems.
• Let a capacitor and an inductor are connected as shown in the figure.
• Let a capacitor be charged Qo at t = 0 sec.
• The moment the circuit is completed, the charge on the capacitor starts decreasing, giving rise to a current in the circuit.
• The angular frequency of the oscillation is given as,

Where L = self-inductance and C = capacitance

• The time period of the oscillation of the charge is given as,

• The charge on the capacitor varies sinusoidally with time as,

⇒ Q = Qocos(ωot)

• The current in the circuit at any time t is given as,

⇒ I = Iosin(ωot)

Where Io = maximum current in the circuit

• The relation between the maximum charge and the maximum current is given as,

⇒ Io = ωoQo

EXPLANATION:

• We know that the angular frequency of the LC oscillation is given as,

     -----(1)

• And the time period of the oscillation of the charge is given as,

     -----(2)

Where L = self-inductance and C = capacitance

By equation 1 and equation 2, the time period of the oscillation of the charge is given as,

     -----(3)

• By equation 3 it is clear that the time period of the oscillation of the charge in the LC oscillation circuit is directly proportional to the square root of the capacitance.
• Therefore if the capacitance of the LC oscillation circuit is increased, then the time period of the oscillation of charge will also increase. Hence, option 4 is correct.