Final answer:
To design an RLC series circuit with a resonance frequency of 1000 rad/s, we use the formula ω₀ = 1/√(LC). Selecting an inductance (L) and solving for capacitance (C), we could use 100 µH and 100 nF respectively. This satisfies the resonance condition while the resistance can be chosen based on the desired damping.
Step-by-step explanation:
The question pertains to the design of an RLC series circuit with a specific undamped natural resonance frequency (ω₀). To construct a circuit that meets the criteria of ω₀ = 1000rad/s, we will use the formula ω₀ = 1/√(LC), where L is the inductance and C is the capacitance. The value of the resistance (R) does not affect the resonance frequency but will influence the bandwidth and damping of the circuit. Therefore, we can choose values for L and C that satisfy the equation ω₀ = 1000 = 1/√(LC). For instance, if we select an L of 100 µH (1 ×10-4 H), we can solve for C as C = 1/(ω₀²L) which yields C = 1/(1 × 106 × 1 ×10-4) Farads = 100 nF. A resistance can then be chosen based on desired damping characteristics.