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Chapter 30: Problem 19

The reactance of an inductor connected with a D.C. voltage is: (a) zero (b) \(\infty\) (c) \(1 \Omega\) (d) none of these

Short Answer

Expert verified
The reactance of an inductor connected with D.C. voltage is zero, hence option (a) is correct.

Step by step solution

01

Understanding the Reactance Concept

Reactance is a property of an inductor when it is subjected to an alternating current (A.C.). The reactance of an inductor is defined as the opposition that the inductor offers to the change of current. The formula for inductive reactance is \( X_L = 2\pi fL \), where \( f \) is the frequency of the current, and \( L \) is the inductance of the coil.
02

Identifying the Type of Voltage

The problem states that the inductor is connected to a direct current (D.C.) voltage. In direct current systems, the frequency \( f \) is zero because D.C. does not vary with time, unlike alternating current (A.C.).
03

Calculating the Reactance for D.C. Voltage

Substituting \( f = 0 \) into the formula for inductive reactance, \( X_L = 2\pi fL \), we get \( X_L = 2\pi \times 0 \times L = 0 \). Therefore, the reactance of an inductor in a D.C. circuit is zero.
04

Selecting the Correct Option

From the solution in Step 3, we see that when the inductor is connected to a D.C. voltage, its reactance is zero. Thus, the correct answer is the option that states 'zero.' Therefore, the correct answer is option (a) zero.

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Key Concepts

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

Direct Current (DC)
In electrical circuits, Direct Current (DC) refers to the flow of electric charge in one constant direction. Unlike alternating current (AC), which periodically reverses direction, DC maintains a steady movement of electrons through the circuit.
This constant electron flow means that the current does not change its direction, creating a stable electrical environment. When it comes to analyzing circuits with inductors, it's important to remember:
  • DC voltage has a frequency of zero. This is because frequency measures how often the current changes direction in a second, and for DC, this number is always zero.
  • Components like resistors behave the same whether powered by AC or DC. However, inductive and capacitive components act quite differently, as they react to changes in current.
Understanding these basic characteristics of DC is crucial when working with electronic components like inductors in such circuits.
Inductor
An inductor is a passive electronic component that stores energy in the form of a magnetic field when electric current flows through it. It generally consists of a coil of wire.
The magnetic field produced by the current flow through the coil gives the inductor its unique properties. Here are some essential attributes of inductors:
  • Inductors resist changes in current. This is due to the principle of self-induction, where a change in current creates a change in the magnetic field, which in turn induces a voltage that opposes the change.
  • The property that allows inductors to oppose the change in current is known as inductance, measured in henrys (H).
  • In AC circuits, inductors exhibit a property called reactance, which is the inductor's opposition to changes in current, but with DC, an inductor acts as a short circuit after the initial energization.
Inductors demonstrate different behaviors depending on whether they are in AC or DC environments, making them versatile components in various electronic applications.
Frequency
Frequency, in the context of electricity, refers to how often the current changes direction each second. It is measured in hertz (Hz). In AC circuits, frequency is a crucial parameter because it affects how components like inductors and capacitors behave.
In a DC circuit, frequency is zero since the current flow is unidirectional and does not oscillate.Important points about frequency include:
  • The formula for calculating the inductive reactance (\( X_L = 2\pi fL \)) illustrates how frequency impacts the reactance of an inductor. When frequency increases, the reactance of the inductor also increases.
  • In DC circuits, since the frequency is zero, the inductive reactance calculates to zero, meaning an inductor offers no resistance to the steady current.
  • Reactance is only applicable in circuits where frequency is greater than zero, reaffirming the role of inductors primarily in AC circuit applications.
Understanding frequency is essential when analyzing how different types of currents interact with electrical components within circuits.

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Most popular questions from this chapter

The average value for half cycle in a \(200 \mathrm{~V}\) A.C. source is : (a) \(180 \mathrm{~V}\) (b) \(200 \mathrm{~V}\) (c) \(220 \mathrm{~V}\) (d) none of these

The average power per unit area at distance of \(2 \mathrm{~m}\) from a small bulb, if the bulb emits \(20 \mathrm{~W}\) of electromagnetic radiation uniformly in all directions, will be : (a) \(0.69 \mathrm{~W} / \mathrm{m}^{2}\) (b) \(0.56 \mathrm{~W} / \mathrm{m}^{2}\) (c) \(0.78 \mathrm{~W} / \mathrm{m}^{2}\) (d) \(0.39 \mathrm{~W} / \mathrm{m}^{2}\)

If a circuit made up of a resistance \(1 \Omega\) and inductance \(0.01 \mathrm{H}\), an alternating emf 200 volt at \(50 \mathrm{~Hz}\) is connected, then the phase difference between the current and the \(\mathrm{emf}\) in the circuit is : (a) \(\tan ^{-1}(\pi)\) (b) \(\tan ^{-1}\left(\frac{\pi}{2}\right)\) (c) \(\tan ^{-1}\left(\frac{\pi}{1}\right)\) (d) \(\tan ^{-1}\left(\frac{\pi}{3}\right)\)

If at a certain instant, the magnetic induction of the electromagnetic wave in vacuum is \(6.7 \times 10^{-12} \mathrm{~T}\), then the magnitude of electric field intensity will be: (a) \(2 \times 10^{-3} \mathrm{~N} / \mathrm{C}\) (b) \(3 \times 10^{-3} \mathrm{~N} / \mathrm{C}\) (c) \(4 \times 10^{-3} \mathrm{~N} / \mathrm{C}\) (d) \(1 \times 10^{-3} \mathrm{~N} / \mathrm{C}\)

Two alternating currents are given by $$ \begin{array}{ll} & I_{1}=I_{0} \sin \omega t \\ \text { and } & I_{2}=I_{0} \cos (\omega t+\phi) \end{array} $$ The ratio of rms values is : (a) \(1: 1\) (b) \(1: \phi\) (c) \(1: 2\) (d) none of these
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