Chapter 31: Problem 9
(a) What is the reactance of a 3.00-H inductor at a frequency of 80.0 Hz? (b) What is the inductance of an inductor whose reactance is 120\(\Omega\) at 80.0 Hz? (c) What is the reactance of a 4.00-\(\mu\)F capacitor at a frequency of 80.0 Hz? (d) What is the capacitance of a capacitor whose reactance is 120 \(\Omega\) at 80.0 Hz?
Short Answer
Step by step solution
Understand Reactance in Inductors
Calculate Reactance of the Inductor
Calculate Inductance from Reactance
Understand Reactance in Capacitors
Calculate Reactance of the Capacitor
Calculate Capacitance from Reactance
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Key Concepts
These are the key concepts you need to understand to accurately answer the question.
Inductive Reactance
- Formula: \(X_L = 2\pi f L\)
- \(f\) is the frequency in hertz (Hz)
- \(L\) is the inductance in henrys (H)
Capacitive Reactance
- Formula: \(X_C = \frac{1}{2\pi f C}\)
- \(f\) is the frequency in hertz (Hz)
- \(C\) is the capacitance in farads (F)
Frequency
- A higher frequency means that the electrical signal oscillates more frequently.
- The response of both inductive and capacitive reactance is highly dependent on frequency.
Inductance
- More inductance means a greater ability to oppose changes in current.
- The formula \(X_L = 2\pi f L\) shows that increasing \(L\) increases \(X_L\).
Capacitance
- In the formula \(X_C = \frac{1}{2\pi f C}\), increasing \(C\) lowers \(X_C\).
- Capacitors are designed to pass AC while blocking DC.