An L-R-C series circuit has L = 0.600 H and C = 3.00 mF. (a) Calculate the angular frequency of oscillation for the circuit when R = 0.

Verified step by step guidance

1. Identify the formula for the angular frequency of oscillation in an L-R-C series circuit without resistance (R=0), which is given by \( \omega = \frac{1}{\sqrt{LC}} \), where L is the inductance and C is the capacitance.
2. Convert the capacitance from millifarads to farads. Recall that 1 mF = 0.001 F.
3. Substitute the values of L and C into the formula. Ensure that the units of L are in henries (H) and C are in farads (F).
4. Calculate the square root of the product LC.
5. Compute the reciprocal of the square root obtained in the previous step to find the angular frequency \( \omega \).

Key Concepts

Angular Frequency

Angular frequency, denoted by ω, is a measure of how quickly an oscillating system cycles through its motion. In the context of an L-R-C circuit, it is calculated using the formula ω = 1/√(LC), where L is the inductance and C is the capacitance. This frequency is expressed in radians per second and is crucial for understanding the oscillatory behavior of the circuit.

Inductance and Capacitance

Inductance (L) is the property of a circuit that opposes changes in current, while capacitance (C) is the ability of a circuit to store charge. In an L-R-C circuit, these two components interact to create oscillations. The values of L and C directly influence the angular frequency of the circuit, determining how fast the energy oscillates between the inductor and capacitor.

Series Circuit

A series circuit is a type of electrical circuit in which components are connected end-to-end, so the same current flows through each component. In an L-R-C series circuit, the inductor, resistor, and capacitor are connected in this manner, affecting the overall impedance and behavior of the circuit. The absence of resistance (R = 0) simplifies the analysis, allowing for ideal oscillations without energy loss.