LC Oscillations

LC Oscillations refers to a situation

• where a circuit contains capacitor and inductor only and charge on the capacitor and current in the circuit, keeps on oscillating harmonically with time.
• where if charge on the capacitor decreases ( in magnitude) with time then current in the circuit increases with time.
• where sum of electrostatic energy in the capacitor and magnetic energy in the inductor, remains constant.

The oscillation frequency of current or charge, depends on the product of the self inductance and capacitanceC in the circuit. If this product is more then the frequency of the oscillation will be lesser.

If the charge and current oscillates with the angular frequency w then the w is equal to the square root of the inverse of the term LC for the circuit. So if both L and C are doubled then the angular frequency will be halved.

The variation of the charge or current with time will be similar to the variation of the position and velocity respectively of a block performing shm while being connected to one end of a spring . Is

• If initially charge on the capacitor is maximum, then after time t , it will be proportional to cosine of wt and current will be proportional to sine of wt.
• If initially current is maximum, then after time t current will be proportional to cosine of wt and the charge will be proportional to sine of wt.

Following are the questions relating to a circuit, which contains only L and C :

1-In the circuit, at time t =0, current is found to be zero and after 2 microseconds, the current grows to it's maximum value. What is the value the term LC for this circuit?

2-In the circuit, at time t =0, current is found to be zero and after 2 microseconds, the current grows to it's maximum value. What is lest value of the time t , when energy stored in the inductor attains half of it's maximum value?

3-In the circuit, initially current is maximum and equals to 10 A. What will be the current when energy stored in the capacitor is three fourth of the total electromagnetic energy of the circuit?

4-In the circuit, initially energy stored in the capacitor and the inductor are same. If this happens again happens 4 microseconds later and never before, then what is the time period of oscillation of the current ?

5-Second derivative of charge with respect to time equals negative of 400 multiplied by the charge. What is the value of the expression LC for the circuit?

Viresh