/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 71 Describe bricfly the physical ba... [FREE SOLUTION] | 91影视

91影视

Describe bricfly the physical basis for mutual inductance.

Short Answer

Expert verified
Mutual inductance occurs when a change in current in one coil induces a voltage in another nearby coil, due to their linked magnetic fields.

Step by step solution

01

Understanding Inductance Basics

To understand mutual inductance, we first need a grasp of basic inductance. Inductance is a property of an electrical conductor by which a change in current through it induces an electromotive force (emf) in both the conductor itself (self-inductance) and in any nearby conductors (mutual inductance).
02

Concept of Magnetic Fields and Flux

When a current flows through a conductor, it generates a magnetic field around it. The amount of magnetic field passing through a given area is called magnetic flux. Therefore, a changing current alters this magnetic flux.
03

Mutual Inductance Definition

Mutual inductance refers to the phenomenon where a change in current in one coil induces a voltage in another nearby coil. This happens due to the magnetic field created by the changing current in the first coil, which then links with the second coil, inducing an emf.
04

Mathematical Expression of Mutual Inductance

Mathematically, the mutual inductance between two coils is defined as the ratio of the induced emf in one coil to the rate of change of current, with respect to the second coil. If coil 1 with current I鈧 influences coil 2, the induced emf (蔚鈧) in coil 2 is given by 蔚鈧 = -M (dI鈧/dt), where M is the mutual inductance.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Inductance
Inductance is a fundamental property of electrical circuits. It's the ability of a conductor to oppose a change in current, measured in henries (H). When current flows through a coil or conductor, it creates a magnetic field around it. If this current changes, the magnetic field also changes, inducing a voltage, or electromotive force (emf), across the same or nearby conductors.
  • Self-inductance: This occurs when the emf is induced in the same conductor that produced the magnetic field.
  • Mutual inductance: Involves more than one conductor, where the magnetic field generated by one affects another nearby.

This property is essential in many electrical devices such as transformers, inductors, and other components of electric circuits. Inductance enables the smooth functioning of circuits, mitigating spikes in current that can damage sensitive components.
Magnetic Fields
Magnetic fields are areas around a magnet or current-carrying conductor where magnetic forces can be detected. The strength and direction of these fields depend on the intensity and direction of the current flowing through the conductor.

To visualize, imagine the small loops of magnetic field lines encircling the conductor as current flows. These loops represent the magnetic field's influence, with their orientation determined by the direction of the current. An important concept is that when a current flows through a conductor, it creates a circular magnetic field around that conductor, following the right-hand rule: if you curl your fingers in the direction of the current, your thumb points in the direction of the magnetic field lines.
  • Field strength increases with higher current.
  • Magnetic fields are central to electromagnetism, affecting nearby conductors and impacting the design and operation of electrical devices.
Electromotive Force
Electromotive force (emf) is a measure of the energy that causes current to flow through a circuit. It is named "force," but it's actually a potential difference, measured in volts. It refers to the voltage developed by any source of electrical energy such as batteries or generators.

In the context of inductance, emf is generated by the changing magnetic field around an electrical conductor. As the current in the conductor changes, this dynamic creates a new emf that can induce current flow even without an initial voltage source. This phenomenon is crucial because it allows for the wireless transfer of energy, as seen in wireless chargers and transformers.
In mathematical terms, the induced emf (5fc) can be expressed as: \[\varepsilon = -L \frac{dI}{dt}\] where \(L\) is the inductance and \( \frac{dI}{dt} \) is the rate of change of current.
Magnetic Flux
Magnetic flux represents the total magnetic field passing through a given area. It鈥檚 calculated as the product of the average magnetic field times the perpendicular area through which it flows, and it's measured in webers (Wb). The concept helps in quantifying the magnetic influence through a specified region.

Consider it similar to how wind might pass through a window鈥攎agnetic flux is like "wind flow," representing the strength and amount of 'magnetic wind' passing through the coil or circuit.
  • An increase in current increases the magnetic field, thereby increasing magnetic flux.
  • Changes in magnetic flux cause an induced electromotive force, per Faraday's Law, essential for understanding mutual inductance and electromagnetic induction.
Mathematically, magnetic flux \(\Phi\) is given by:\[\Phi = B \cdot A \cdot \cos(\theta)\]where \(B\) is the magnetic field, \(A\) is the area the field penetrates, and \(\theta\) is the angle between the field lines and the perpendicular to the surface.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Suppose that we are designing a cardiac pacemaker circuit. The circuit is required to deliver pulses of 1 -ms duration to the heart. which can be modeled as a \(500-\Omega\) resistance. The peak amplitude of the pulses is required to be 5 V. However, the battery delivers only \(2.5 \mathrm{V}\). Therefore, we decide to charge two equal-value capacitors in parallel from the \(2.5 \cdot V\) battery and then switch the capacitors in series with the heart during the 1 -ms pulse. What is the minimum value of the capacitances required so the output pulse amplitude remains between \(4.9 \mathrm{V}\) and \(5.0 \mathrm{V}\) throughout its \(1-\mathrm{ms}\) duration? If the pulses occur once every second, what is the average current drain from the battery? Use approximate calculations, assuming constant current during the output pulse. Find the ampere-hour rating of the battery so it lasts for five years.

Briefly discuss how inductors are constructed.

We have a \(1-\mu \mathrm{F}\) capacitor with \(200 \mathrm{V}\) between its terminals. Determine the magnitude of the net charge stored on each plate and the total nct charge on both plates.

A microphone can be formed from a parallel plate capacitor arranged so the acoustic pressure of the sound wave affects the distance between the plates Suppose we have such a microphone in which the plates have an area of \(10 \mathrm{cm}^{2}\). the dielectric is air, and the distance between the plates is a function of time given by $$d(t)=100+0.5 \cos (5000 t) \mu \mathrm{m}$$ A constant voltage of \(200 \mathrm{V}\) is applied to the plates. Determine the current through the capacitance as a function of time by using the approximation \(1 /(1+x) \cong 1-x\) for \(x<<1 .\) (The argument of the sinusoid is in radians.)

A \(20-\mu \mathrm{F}\) capacitor has a voltage given by \(v(t)=10-10 \operatorname{csp}(-2000 t) \mathrm{V} .\) Find the power at \(t=0\) and state whether the power flow is into or out of the capacitor. Repeat for \(t_{2}=0.5 \mathrm{ms}\)

See all solutions

Recommended explanations on Physics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.