Final answer:
To find the angular frequency at which a 4.40 μF capacitor has the same reactance as a 9.00 mH inductor, we set the capacitor's reactance equal to the inductor's reactance and solve for ω, yielding approximately 1,516 radians per second.
Step-by-step explanation:
The question asks about finding an angular frequency at which a capacitor's reactance is equal to an inductor's reactance. To solve for the angular frequency, we use the formula for reactance of capacitors (XC = 1 / (ωC)) and inductors (XL = ωL), where ω is the angular frequency, C is the capacitance, and L is the inductance. Since we want the reactances to be equal, we set 1 / (ωC) equal to ωL and solve for ω.
1 / (ω * 4.40 × 10-6 F) = ω * 9.00 × 10-3 H
Solving for ω gives:
ω2 = 1 / (L * C)
ω = √(1 / (4.40 × 10-6 F * 9.00 × 10-3 H))
ω ≈ 1,516 rad/s