What is the inductance of an inductor whose reactance is 120 Ω at 80.0 Hz?

Verified step by step guidance

1. Understand the concept of inductive reactance, which is the opposition that an inductor presents to alternating current. It is given by the formula: $X=\omega L$, where $X$ is the reactance, $\omega$ is the angular frequency, and $L$ is the inductance.
2. Calculate the angular frequency $\omega$ using the formula: $\omega =2\pi f$, where $f$ is the frequency. Substitute $f$ with 80.0 Hz.
3. Substitute the given reactance value $X=120$ Ω and the calculated angular frequency $\omega$ into the reactance formula: $X=\omega L$.
4. Rearrange the formula to solve for inductance $L$: $L=\frac{X}{\omega }$.
5. Substitute the values of $X$ and $\omega$ into the rearranged formula to find the inductance $L$.

Key Concepts

Inductive Reactance

Inductive reactance is the opposition that an inductor presents to alternating current, due to the magnetic field created around it. It is given by the formula X_L = 2πfL, where X_L is the reactance, f is the frequency, and L is the inductance. This concept is crucial for understanding how inductors behave in AC circuits.

Inductance

Inductance is a property of an electrical conductor that quantifies its ability to induce an electromotive force when the current flowing through it changes. It is measured in henries (H) and is a fundamental concept in electromagnetism, affecting how circuits respond to changes in current and voltage.

Frequency

Frequency refers to the number of cycles per second of an alternating current, measured in hertz (Hz). It is a key parameter in AC circuits, influencing the reactance of inductors and capacitors. Understanding frequency is essential for calculating reactance and determining the behavior of AC circuit components.