1. **Problem Statement:** Determine if the results from the calculations of inductive and capacitive reactance make sense and explain how a capacitor reacts to an increase in frequency. 2. **Formulas Used:** - Inductive Reactance: $$X_{L} = 2\pi f L$$ - Capacitive Reactance: $$X_{C} = \frac{1}{2\pi f C}$$ 3. **Explanation of Reactance Behavior:** - For an inductor, reactance increases with frequency because a faster changing magnetic field induces a higher back EMF, opposing current flow. - For a capacitor, reactance decreases with frequency because higher frequency means less time for charge to accumulate, allowing more current to pass. 4. **Inductive Reactance Calculations:** - At $$f_1 = 60$$ Hz, $$L = 0.01$$ H: $$X_{L1} = 2 \times 3.14159 \times 60 \times 0.01 = 3.77\ \Omega$$ - At $$f_2 = 1000$$ Hz, $$L = 0.01$$ H: $$X_{L2} = 2 \times 3.14159 \times 1000 \times 0.01 = 62.83\ \Omega$$ 5. **Capacitive Reactance Calculations:** - At $$f_1 = 60$$ Hz, $$C = 10 \times 10^{-6}$$ F: $$X_{C1} = \frac{1}{2 \times 3.14159 \times 60 \times 10 \times 10^{-6}} = 265.26\ \Omega$$ - At $$f_2 = 1000$$ Hz, $$C = 10 \times 10^{-6}$$ F: $$X_{C2} = \frac{1}{2 \times 3.14159 \times 1000 \times 10 \times 10^{-6}} = 15.92\ \Omega$$ 6. **Interpretation:** - The inductive reactance increased from 3.77 to 62.83 ohms as frequency increased, which matches the theory. - The capacitive reactance decreased from 265.26 to 15.92 ohms as frequency increased, confirming that capacitors offer less impedance at higher frequencies. 7. **Conclusion:** - Yes, the results make sense and align with the physical behavior of inductors and capacitors. - A capacitor's impedance decreases with increasing frequency, meaning it allows more current to pass at higher frequencies.