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SI unit of inductance can be written as (A) Weber/Ampere (B) Joule/Ampere \(^{2}\) (C) Ohm/Second (D) All of the above

Short Answer

Expert verified
The correct SI unit of inductance is (A) Weber/Ampere, which can be represented as \(1 \, \text{Henry} = 1 \, \dfrac{\text{Weber}}{\text{Ampere}}\).

Step by step solution

01

Recall the definition of inductance

Inductance is a property of an electrical circuit that opposes any change in current. It depends on the physical characteristics of a conductor and the magnetic field around it. The symbol for inductance is \(L\), and its SI unit is called the Henry (H).
02

Express the SI unit of inductance in terms of basic units

Recall that the definition of Henry can be written in terms of other SI units: \[1 \, \text{Henry} = 1 \, \dfrac{\text{Weber} \cdot \text{Volt}}{\text{Ampere}^2}\] We also know that Volt/Amper = Ohm and Weber = Volt * second. So, the expression becomes: \[1 \, \text{Henry} = 1 \, \dfrac{(\text{Volt} \cdot \text{Second}) \cdot \text{Ohm}}{\text{Ampere}^2}\]
03

Simplify the expression and compare with the given options

The simplified expression for the SI unit of inductance is: \[1 \, \text{Henry} = 1 \, \dfrac{\text{Weber}}{\text{Ampere}}\] Now, let's compare this expression with the given options: (A) Weber/Ampere: This matches our simplified expression, so this option is correct. (B) Joule/Ampere²: This option does not match our simplified expression, so this option is incorrect. (C) Ohm/Second: This option does not match our simplified expression, so this option is incorrect. (D) All of the above: Since only option (A) is correct, this option is also incorrect.
04

Identify the correct answer

The correct answer is (A) Weber/Ampere. This is the correct SI unit of inductance.

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Key Concepts

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

SI Units
SI Units form the foundation of scientific measurements across various disciplines. The International System of Units (SI) is the globally accepted metric used to standardize measurements. This system helps foster consistency and precision in scientific communication. Every physical quantity, like time, length, or temperature, has a corresponding SI unit.
For inductance, the SI unit used is the Henry (H). This facilitates uniformity, ensuring that calculations and understandings remain consistent globally.
  • Time: Second (s)
  • Length: Meter (m)
  • Current: Ampere (A)
When you're working with equations in physics or engineering, recognizing units like Henry in the context of inductance helps clarify calculations and their outcomes. With the widespread adoption of SI units, a mutual understanding is in place, driving innovation and communication forward.
Henry
The Henry is the SI unit for inductance, symbolized by the letter H. Named after Joseph Henry, an American scientist who made significant contributions to electromagnetism, the Henry defines the amount of inductance in an electrical circuit.
Simply put, inductance is a measure of a component's ability to store energy in a magnetic field when a current flows through it. When a current changes, the energy stored can oppose or enhance the change in current.
  • If a circuit has an inductance of one Henry, then one volt will be induced when the current changes at one ampere per second.
  • Henry is expressed in terms of other electrical and magnetic units such as Weber per Ampere (Wb/A).
Understanding Henry as a unit is crucial for those studying electrical and magnetic circuits. It is fundamental for analyzing and designing circuits that include components like inductors and transformers.
Electrical Circuits
Electrical circuits serve as the backbone for a plethora of devices and applications in our daily lives. An electrical circuit is essentially a path in which electrons from a voltage or current source flow.
Comprising various components like resistors, capacitors, and inductors, each has its role. These components work together to perform functions such as powering devices, charging batteries, or transforming energy from one form to another.
  • Inductors: Components that rely heavily on the concept of inductance, resisting changes in current.
  • Resistors: Used to resist the flow of current and manage power levels.
  • Capacitors: Store and release electrical energy.
Understanding circuits is essential for engineers and technologists, enabling the construction and maintenance of efficient electrical systems. Insights into how current flows and how devices use and transform energy are important for innovation.
Magnetic Field
Magnetic fields are invisible fields exerted by magnets or moving charges, providing a powerful influence on objects within their reach. Any current-carrying conductor generates a magnetic field, and this is a fundamental concept in electromagnetism.
In the context of inductance, a magnetic field plays a pivotal role. When current flows through a coil or inductor, it produces a magnetic field that grows stronger as more current flows. Conversely, changing the current will affect the magnetic field and induce a voltage in nearby conductors, a principle crucial in transformers and wireless power technologies.
  • Magnetic fields are typically measured in Tesla (T) or Gauss (G).
  • Understanding their behavior helps in devising solutions in electronics, communication, and medical imaging.
The interplay between electricity and magnetism, expressed through magnetic fields, forms the backbone of modern technology, enabling devices to communicate, sense, and operate effectively.

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Most popular questions from this chapter

In an oscillating LC circuit, the maximum charge on the capacitor is \(Q .\) The charge on the capacitor when the energy is stored equally between the electric and magnetic field is (A) \(\frac{Q}{2}\) (B) \(\frac{Q}{\sqrt{3}}\) (C) \(\frac{Q}{\sqrt{2}}\) (D) \(Q\)

A varying magnetic flux linking a coil is given by \(\phi=3 t^{2}\). The magnitude of induced EMF in the loop at \(t=3 \mathrm{~s}\) is (A) \(3 \mathrm{~V}\) (B) \(9 \mathrm{~V}\) (C) \(18 \mathrm{~V}\) (D) \(27 \mathrm{~V}\)

A block is attached to the ceiling by a spring that has a force constant \(k=200 \mathrm{~N} / \mathrm{m} .\) A conducting rod is rigidly attached to the block. The combined mass of the block and the rod is \(m=0.3 \mathrm{~kg}\). The rod can slide without friction along two vertical parallel rails, which are a distance \(\ell=1 \mathrm{~m}\) apart. A capacitor of known capacitance \(C=500 \mu \mathrm{F}\) is attached to the rails by the wires. The entire system is placed in a uniform magnetic field \(B=20 \mathrm{~T}\) directed as shown. Find the angular frequency (in \(\mathrm{rad} / \mathrm{s}\) ) of the vertical oscillations of the block. Neglect the self-inductance and electrical resistance of the rod and all wires.

A small square loop of wire of side \(\ell\) is placed inside a large square loop of wire of side \(L(L>>\ell)\). The loops are coplanar and their centres coincide. The mutual inductance of the system is proportional to (A) \(\frac{l}{L}\) (B) \(\frac{l^{2}}{L}\) (C) \(\frac{L}{l}\) (D) \(\frac{L^{2}}{l}\)

Heat generated (in \(\mathrm{kJ}\) ) through the ring till the instant when ring starts toppling is (A) \(\frac{1}{3 \pi}\) (B) \(\frac{2}{\pi}\) (C) \(\frac{2}{3 \pi}\) (D) \(\frac{1}{\pi}\)

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