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Chapter 6: Problem 4

Does inductance depend on current, frequency, or both? What about inductive reactance?

Short Answer

Expert verified
Inductance depends on neither current nor frequency; inductive reactance depends on both frequency and inductance.

Step by step solution

01

Understanding Inductance

Inductance, measured in henries (H), is a property of an electrical component that opposes changes in current. It depends on the physical characteristics of the component such as the number of turns in a coil, the cross-sectional area, and the core material, but not on the current (I) or frequency (f).
02

Understanding Inductive Reactance

Inductive reactance, denoted by \( X_L \), is the opposition a component provides to the change in current due to its inductance in an AC circuit. It is calculated using the formula \( X_L = 2\pi f L \), where \( f \) is the frequency and \( L \) is the inductance.
03

Examining Dependence of Inductive Reactance

From the formula \( X_L = 2\pi f L \), inductive reactance depends on both the frequency (f) and the inductance (L). Frequency directly influences the value of \( X_L \), meaning higher frequency increases inductive reactance.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Inductive Reactance
Inductive Reactance is an important concept to understand in AC circuits. It essentially describes how much an inductor resists the flow of varying current. The resistance offered is not like a resistor, which is constant, but changes with frequency. Let's delve into its calculation:
  • Inductive Reactance, represented by \( X_L \), is given by the formula \( X_L = 2\pi f L \). Here, \( f \) stands for frequency in hertz, and \( L \) is the inductance in henries.
  • This means that as the frequency increases, the opposition to current flow also increases, resulting in higher inductive reactance.
  • The unit of inductive reactance is ohms (惟), just like regular resistance.
Knowing the behavior of inductive reactance helps in designing circuits and managing how they respond to different frequencies.
Frequency Dependence
Understanding Frequency Dependence is crucial when dealing with components that react to changing currents. In essence, it describes how certain electrical parameters change when the frequency of the supply current changes. Inductors, as components, are greatly influenced by this factor.
  • Higher frequencies make reactive components like inductors and capacitors exhibit greater changes compared to lower frequencies.
  • For inductors, a higher frequency means higher inductive reactance, which opposes the alternating current more.
  • Engineers must consider frequency responses when designing circuits, especially for applications like filters or communication systems.
The dependence on frequency is vital for AC circuit functionalities and efficiency, ensuring devices operate optimally within their designated frequency ranges.
AC Circuits
AC Circuits are a realm where alternating current flows, meaning the current periodically reverses direction. Many household and industrial electrical systems are designed to run on AC for various reasons.
  • Unlike DC circuits, AC circuits naturally suit transformers, allowing easy voltage transformation and long-distance power transmission.
  • Components in AC circuits, like inductors and capacitors, exhibit unique characteristics due to the alternating nature of current.
  • Adjustments to design and component selection might be required to effectively manage these characteristics for a given application.
Understanding AC circuits is essential for fields like power engineering, telecommunications, and any technology or system relying on alternating current.

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Most popular questions from this chapter

A powerful induction cannon can be made by placing a metal cylinder inside a solenoid coil. The cylinder is forcefully expelled when solenoid current is turned on rapidly. Use Faraday's and Lenz's laws to explain how this works. Why might the cylinder get live/hot when the cannon is fired?

A \(0.250 \mathrm{~m}\) radius, 500 -turn coil is rotated one-fourth of a revolution in \(4.17 \mathrm{~ms}\), originally having its plane perpendicular to a uniform magnetic field. (This is 60 rev/s.) Find the magnetic field strength needed to induce an average emf of \(10,000 \mathrm{~V}\).

Would you use a large inductance or a large capacitance in series with a system to filter out low frequencies, such as the \(100 \mathrm{~Hz}\) hum in a sound system? Explain.

What capacitance should be used to produce a \(2.00 \mathrm{M} \Omega\) reactance at \(60.0 \mathrm{~Hz} ?\)

(a) Calculate the self-inductance of a \(50.0 \mathrm{~cm}\) long, \(10.0 \mathrm{~cm}\) diameter solenoid having 1000 loops. (b) How much energy is stored in this inductor when \(20.0 \mathrm{~A}\) of current flows through it? (c) How fast can it be turned off if the induced emf cannot exceed \(3.00 \mathrm{~V}\) ?
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