What is the reactance of a 3.00-H inductor at a frequency of 80.0 Hz?

Verified step by step guidance

1. Understand the concept of inductive reactance: Inductive reactance is the opposition that an inductor offers to the change in current. It is dependent on the frequency of the alternating current and the inductance of the coil.
2. Recall the formula for inductive reactance: The inductive reactance \( X_L \) is given by the formula \( X_L = 2\pi f L \), where \( f \) is the frequency and \( L \) is the inductance.
3. Identify the given values: From the problem, we have the inductance \( L = 3.00 \) H and the frequency \( f = 80.0 \) Hz.
4. Substitute the given values into the formula: Replace \( f \) and \( L \) in the formula \( X_L = 2\pi f L \) with the given values to find the reactance.
5. Calculate the reactance: Perform the multiplication and use the value of \( \pi \approx 3.14159 \) to compute the reactance \( X_L \).

Key Concepts

Inductive Reactance

Inductive reactance is the opposition that an inductor presents to alternating current due to its inductance. It is calculated using the formula X_L = 2πfL, where X_L is the inductive reactance, f is the frequency of the AC signal, and L is the inductance. This concept is crucial for understanding how inductors affect AC circuits.

Frequency

Frequency refers to the number of cycles per second of an alternating current, measured in Hertz (Hz). It is a fundamental parameter in AC circuits that influences reactance and impedance. In this context, the frequency determines how quickly the current changes direction, affecting the reactance of the inductor.

Inductance

Inductance is a property of an electrical conductor that quantifies its ability to induce voltage when the current flowing through it changes. Measured in henries (H), inductance is a key factor in determining the reactance of an inductor in AC circuits. A higher inductance results in greater opposition to changes in current.