In an LC circuit, the values of L and C are 5.0 × 10^-2 H and 5.0 × 10^-6 F, respectively. At t = 0 all of the energy is stored in the capacitor. Then the angular frequency of the LC oscillations in the circuit (in radians/s) is:

Concept:

LC oscillation:

• An LC circuit is a type of electric circuit that is made up of an inductor which is expressed by the letter L, and a capacitor, represented by the letter C.
• The electric current and the charge on the capacitor in the circuit undergo electrical LC oscillations when a charged capacitor is connected to an inductor.

• LC circuit is also known as a tank circuit, a resonant circuit, or a tuned circuit.
• The angular frequency of the LC oscillation, \(ω =\frac{1}{\sqrt{LC}}\)
• Here, angular frequency, ω = 2πf  where , f = linear frequency

Calculation:

Given,

The capacitance of the capacitor, C = 5.0 × 10-6 F

The inductance of the inductor, L = 5.0 × 10-2 H 

The angular frequency of the LC oscillation in the circuit, 

\(ω =\frac{1}{\sqrt{LC}}\)

\(ω =\frac{1}{\sqrt{5\times 10^{-2}\times 5\times 10^{-6}}}=2\times 10^{3} rad/s\)

Hence, the angular frequency of the LC oscillations in the circuit (in radians/s) is: 2.0 × 103