Final answer:
To find the frequency at which an RLC circuit is purely reactive, calculate the resonant angular frequency using the formula ω₀ = 1 / √(LC), which yields 353.55 rad/s for the given values of L = 400mH and C = 20μF.
Step-by-step explanation:
The student is asking to determine the frequency, in radians per second, at which an RLC (Resistor-Inductor-Capacitor) circuit is purely reactive. This occurs at the resonant frequency where the reactance of the capacitor equals the reactance of the inductor. The formula to calculate the resonant angular frequency (ω₀) is:
ω₀ = 1 / √(LC)
First, convert the given values to their base units:
- Capacitance (C): 20μF = 20 × 10^{-6} F
- Inductance (L): 400mH = 0.4 H
Now plug these values into the formula to find the resonant angular frequency:
ω₀ = 1 / √(0.4 H × 20 × 10^{-6} F) = 1 / √(8 × 10^{-6} H·F) = 1 / √(8 × 10^{-6}) = 1 / (2.828 × 10^{-3})
ω₀ = 353.55 rad/s
This is the frequency at which the circuit is purely reactive and resonance occurs.