Ch 31: Alternating Current

Young & Freedman Calc - University Physics 15th Edition

Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Not the one you use?Change textbook

Young & Freedman Calc 15th Edition

Ch 31: Alternating Current

Problem 5a

Chapter 31, Problem 5a

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

Verified step by step guidance

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.

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.

Identify the given values: From the problem, we have the inductance \( L = 3.00 \) H and the frequency \( f = 80.0 \) Hz.

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.

Calculate the reactance: Perform the multiplication and use the value of \( \pi \approx 3.14159 \) to compute the reactance \( X_L \).

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.

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Related Practice

Textbook Question

(a) Compute the reactance of a 0.450-H inductor at frequencies of 60.0 Hz and 600 Hz. (b) Compute the reactance of a 2.50-μF capacitor at the same frequencies. (c) At what frequency is the reactance of a 0.450-H inductor equal to that of a 2.50-μF capacitor?

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Textbook Question

A capacitor is connected across an ac source that has voltage amplitude 60.0 V and frequency 80.0 Hz. What is the phase angle Φ for the source voltage relative to the current? Does the source voltage lag or lead the current?

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Textbook Question

A capacitor is connected across an ac source that has voltage amplitude 60.0 V and frequency 80.0 Hz. What is the capacitance C of the capacitor if the current amplitude is 5.30 A?

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Textbook Question

A capacitance C and an inductance L are operated at the same angular frequency. (a) At what angular frequency will they have the same reactance? (b) If L = 5 00 mH and C = 3.50 μF, what is the numerical value of the angular frequency in part (a), and what is the reactance of each element?

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Textbook Question

The voltage across the terminals of an ac power supply varies with time according to Eq. (31.1) v = Vcosωt. The voltage amplitude is V = 45.0 V. What are (a) the root-mean-square potential difference V_rms and (b) the average potential difference V_av between the two terminals of the power supply?

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Textbook Question

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