Ohm's Law

12 Key excerpts on "Ohm's Law"

• 

  No longer available |Learn more

  Laws and Theories of Physics

  • (Author)
  • 2014(Publication Date)
  • Learning Press

    (Publisher)

  In order to fix Kirchhoff's voltage law for circuits containing inductors, an effective potential drop, or electromotive force (emf), is associated with each inductance of the circuit, exactly equal to the amount by which the line integral of the electric field is not zero by Faraday's law of induction. 3. Ohm's Law V, I, and R, the parameters of Ohm's Law Ohm's Law states that the current through a conductor between two points is directly proportional to the potential difference or voltage across the two points, and inversely proportional to the resistance between them. The mathematical equation that describes this relationship is: ________________________ WORLD TECHNOLOGIES ________________________ where I is the current through the resistance in units of amperes, V is the potential difference measured across the resistance in units of volts, and R is the resistance of the conductor in units of ohms. More specifically, Ohm's Law states that the R in this relation is constant, independent of the current. The law was named after the German physicist Georg Ohm, who, in a treatise published in 1827, described measurements of applied voltage and current through simple electrical circuits containing various lengths of wire. He presented a slightly more complex equation than the one above to explain his experimental results. The above equation is the modern form of Ohm's Law. In physics, the term Ohm's Law is also used to refer to various generalizations of the law originally formulated by Ohm. The simplest example of this is: where J is the current density at a given location in a resistive material, E is the electric field at that location, and σ is a material dependent parameter called the conductivity. This reformulation of Ohm's Law is due to Gustav Kirchhoff.

  Sign up to read

  Learn more about book
• 

  eBook - ePub

  Learn Audio Electronics with Arduino

  Practical Audio Circuits with Arduino Control

  • Charlie Cullen(Author)
  • 2020(Publication Date)
  • Focal Press

    (Publisher)

  For a higher resistance value, the reduction in current flow means more charge is now concentrated at one end of the resistor as it cannot flow easily to the other end. This increased resistance creates an increased imbalance in charge, which creates a higher potential difference between the two ends of the wire as a result. We know that the current does not change because the number of electrons stays the same, the only difference is where the electrons are located. Thus, we can see that increasing R increases V, so we can derive V o l t a g e, V = I R. Scales, symbols and equations In chapter 1, we learned that fundamental electronics equations are not mathematically complex, but the scales and quantities involved can take time to learn. Ohm’s Law defines the simple mathematical relationship between the three fundamental elements of voltage (V), current (I) and resistance (R), but the symbols involved can initially appear a little confusing. The letter (I) is used for current partly because it was originally discovered by André-Marie Ampére, who as a French speaker named the quantity Intensité du Courant (Current Intensity). In addition, electrical charge is measured in coulombs (C), which would also create a confounding between terms! As you progress through the book you will find that scales and symbols often take more time to learn than equations, so terms will be explained whenever they are first introduced. Ohm’s Law is a simple equation to work with and forms the basis of all electrical circuit analysis

  Sign up to read

  Learn more about book
• 

  eBook - PDF

  Delmar's Standard Textbook of Electricity

  • Stephen Herman(Author)
  • 2019(Publication Date)
  • Cengage Learning EMEA

    (Publisher)

  He found that if the resistance of a circuit remained constant and the voltage increased, there was a corresponding proportional increase of current. Similarly, if the resistance remained constant and the voltage decreased, there would be a proportional decrease of current. He also found that if the voltage remained constant and the resistance in-creased, there would be a decrease of current; and if the voltage remained constant and the re-sistance decreased, there would be an increase of current. This finding led Ohm to the conclusion that in a DC circuit, the current is directly proportional to the voltage and inversely propor-tional to the resistance. 1 horsepower = 1 horsepower = 1 watt = 1 watt = 1 wattsecond = 1 BTU-hr = 1 cal/s = 1 ft-lb/s = 1 BTU = 1 joule = 1 cal = 746 watts 550 ft-lb/s 0.00134 horsepower 3.412 BTU/hr 1 joule 0.293 Whr 4.19 watts 1.36 watts 1050 joules 0.2388 cal 4.187 joules FIGURE 2–15 Common power units. Copyright 2020 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. UNIT 2 Electrical Quantities and Ohm’s Law 63 Because Ohm’s law is a statement of proportion, it can be expressed as an algebraic formula when standard values such as the volt, the ampere, and the ohm are used. The three basic Ohm’s law formulas are E 5 I 3 R I 5 E R EXAMPLE 2–1 An elevator must lift a load of 4000 lb to a height of 50 ft in 20 s.

  Sign up to read

  Learn more about book
• 

  eBook - ePub

  College Physics Essentials, Eighth Edition

  Electricity and Magnetism, Optics, Modern Physics (Volume Two)

  • Jerry D. Wilson, Anthony J. Buffa, Bo Lou(Authors)
  • 2019(Publication Date)
  • CRC Press

    (Publisher)

  only if R is constant .

  ▲ Figure 17.11 Ohm’s law If an object obeys Ohm’s law (constant resistance), a plot of voltage versus current is linear with a slope equal to R, the object’s resistance.

  Δ V = I R   ( Ohm’s   law:   R   is   constant )	(17.3)

  Keep in mind, then, that Ohm’s “law” is not a fundamental law in the same sense as, for example, the law of conservation of energy. There is no “law” that states that materials must have constant resistance. Indeed, many advances in electronics are based on materials such as semiconductors, which have variable resistance or nonlinear (non-ohmic) voltage-current relationships.

  Example 17.3 shows how the resistance of the human body can make the difference between life and death. Example 17.3: Danger in the House – Human Resistance

  Any room in a house that is exposed to water and electrical voltage can present hazards. (See the discussion of electrical safety in Section 18.5.) For example, suppose a person steps out of a shower and inadvertently touches an exposed 120-V wire (perhaps a frayed cord on a hair dryer) with a finger, thus creating a complete circuit though the body to the wet floor. The human body, when wet, can have an electrical resistance as low as 300 Ω . Using this value, estimate the current in that person’s body.

  Thinking It Through .

  Sign up to read

  Learn more about book
• 

  eBook - ePub

  Classical Electromagnetism in a Nutshell

  • Anupam Garg(Author)
  • 2012(Publication Date)
  • Princeton University Press

    (Publisher)

  Our second theme, therefore, will be to describe a few selected sources of emf. Our description will have very much of a “how things work” flavor, since the physics of the devices is highly varied and outside the theory of electromagnetism per se. An understanding of these sources is nevertheless very useful, as the notion of an emf tends to remain somewhat mysterious without it.

  FIGURE 17.1. Current through (a) a general conductor, (b) a uniform wire.

  The discussion of emf and Ohm’s law naturally leads to our last theme, linear circuits. We will discuss these very briefly, mainly to highlight the approximations and the limits of their validity.

  110 Ohm’s law

  The fundamental feature of metals is the existence of free or delocalized electrons which can conduct electricity. To solve Maxwell’s equations in the presence of current-carrying bodies, one needs a constitutive equation connecting the current to the fields in the body. This is provided by Ohm’s law, which Ohm discovered through extensive experiments. For a body carrying a steady current, the law takes the local form

  Here, j and E are the current density and electric field at any point in the body, and σ is known as the conductivity of the material in question. It is necessarily a positive quantity, since the electric field inside the body accelerates the electrons and increases their kinetic energy. In steady state, this increased energy must be dissipated as heat. The rate of dissipation per unit volume is easily shown to be and its positivity implies σ > 0.

  Conductivity has dimensions of inverse time in the Gaussian system and may therefore be quoted in sec−1 . It is equally common to give the inverse of the conductivity, known as the resistivity:

  This has units of sec in the Gaussian system and ohm m in the SI system. One ohm m is a rather high resistivity, however, so one often sees the derived unit micro-ohmcentimeter, written μ ohm cm. The conversion factor for resistivity is

  Ohm’s law also applies to materials other than metals, e.g., semiconductors and electrolytic solutions. When these are included, resistivities can vary over a wide range. At 273 K, the resistivities of pure copper, tin, and bismuth are 1.6, 11, and 110, all in μ ohm cm, that of germanium is 200 ohm cm, and of seawater is ~25 ohm cm (note the missing micro). By varying the temperature and doping, semiconductor resistivities can be made to vary over 13 orders of magnitude, from 10−2 to 1011 ohm cm. We shall develop a physical model of conduction in chapter 18

  Sign up to read

  Learn more about book
• 

  eBook - PDF

  Physics

  • John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler(Authors)
  • 2021(Publication Date)
  • Wiley

    (Publisher)

  Conventional current is the hypothetical flow of positive charges that would have the same effect in a circuit as the movement of negative charges that actually does occur. I = Δq _ Δt (20.1) 20.2 Ohm’s Law The definition of electrical resistance R is R = V/I, where V (in volts) is the voltage applied across a piece of material and I (in amperes) is the current through the material. Resistance is measured in volts per ampere, a unit called an ohm (Ω). If the ratio of the voltage to the current is constant for all values of voltage and cur- rent, the resistance is constant. In this event, the definition of resist- ance becomes Ohm’s law, Equation 20.2. V _ I = R = constant or V = IR (20.2) 20.3 Resistance and Resistivity The resistance of a piece of mate- rial of length L and cross-sectional area A is given by Equation 20.3, where ρ is the resistivity of the material. The resistivity of a material depends on the temperature. For many materials and limited tem- perature ranges, the temperature dependence is given by Equation 20.4, where ρ and ρ 0 are the resistivities at the temperatures T and T 0 , respectively, and  is the temperature coefficient of resistivity. The temperature dependence of the resistance R is given by Equa- tion 20.5, where R and R 0 are the resistances at the temperatures T and T 0 , respectively. R = ρ L _ A (20.3) ρ = ρ 0 [1 + α(T − T 0 )] (20.4) R = R 0 [1 + α(T − T 0 )] (20.5) 20.4 Electric Power When electric charge flows from point A to point B in a circuit, leading to a current I, and the voltage between the points is V, the electric power associated with this current and voltage is given by Equation 20.6a. For a resistor, Ohm’s law applies, and it follows that the power delivered to the resistor is also given by either Equation 20.6b or 20.6c.

  Sign up to read

  Learn more about book
• 

  eBook - PDF

  Cutnell & Johnson Physics, P-eBK

  • John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler, Heath Jones, Matthew Collins, John Daicopoulos, Boris Blankleider(Authors)
  • 2020(Publication Date)
  • Wiley

    (Publisher)

  I = Δq Δt (20.1) 20.2 Solve problems using Ohm’s law for a simple series circuit. The definition of electrical resistance R is R = V /I, where V (in volts) is the voltage applied across a piece of material and I (in amperes) is the current through the material. Resistance is measured in volts per ampere, a unit called an ohm (Ω). If the ratio of the voltage to the current is constant for all values of voltage and current, the resistance is constant. In this event, the definition of resistance becomes Ohm’s law, equation 20.2. V I = R = constant or V = IR (20.2) 20.3 Relate resistance and resistivity. The resistance of a piece of material of length L and cross‐sectional area A is given by equation 20.3, where  is the resistivity of the material. The resistivity of a material depends on the temperature. For many materials and limited temperature ranges, the temperature dependence is given by equation 20.4, where  and  0 are the resistivities at the temperatures T and T 0 , respectively, and  is the temperature coefficient of resistivity. The temperature dependence of the resistance R is given by equation 20.5, where R and R 0 are the resistances at the temperatures T and T 0 , respectively. R =  L A (20.3)  =  0 [ 1 +  ( T - T 0 )] (20.4) R = R 0 [ 1 +  ( T - T 0 )] (20.5) 20.4 Solve problems involving electric power. When electric charge flows from point A to point B in a circuit, leading to a current I, and the voltage between the points is V, the electric power associated with this current and voltage is given by equation 20.6a. For a resistor, Ohm’s law applies, and it follows that the power delivered to the resistor is also given by either equation 20.6b or 20.6c. P = IV (20.6a) P = I 2 R (20.6b) P = V 2 R (20.6c) 20.5 Solve ac circuit problems for current and power.

  Sign up to read

  Learn more about book
• 

  eBook - PDF

  RealTime Physics: Active Learning Laboratories, Module 3

  Electricity and Magnetism

  • David R. Sokoloff, Priscilla W. Laws(Authors)
  • 2012(Publication Date)
  • Wiley

    (Publisher)

  LAB 6: VOLTAGE IN SIMPLE DC CIRCUITS AND OHM’S LAW 105 LAB 6: VOLTAGE IN SIMPLE DC CIRCUITS AND OHM’S LAW* I have a strong resistance to understanding the relationship between voltage and current. —Anonymous introductory physics student OBJECTIVES • To learn to apply the concept of potential difference (voltage) to explain the action of a battery in a circuit. • To understand how potential difference (voltage) is distributed in different parts of a series circuit. • To understand how potential difference (voltage) is distributed in different parts of a parallel circuit. • To understand the quantitative relationship between potential difference and current for a resistor (Ohm’s law). OVERVIEW In the last two labs you explored currents flowing at different points in series and parallel circuits. You saw that in a series circuit, the same current flows through all elements. You also saw that in a parallel circuit, the current divides among the branches so that the total current flowing through the battery equals the sum of the currents flow- ing through each of the branches. You have also observed that when two or more parallel branches are con- nected directly across a battery, making a change in one branch does not affect the current flowing in the other branch(es), while changing one part of a series circuit changes the current flowing in all parts of that series circuit. Name Date Partners *Some of the activities in this lab have been adapted from those designed by the Physics Edu- cation Group at the University of Washington, as adapted for Workship Physics Module 4. BATTERY + – SOFTWARE & TECHNOLOGY Differential Voltage Sensor VISUAL SOFTWARE & TECHNOLOGY CURRENT 800 mA Max + –

  Sign up to read

  Learn more about book
• 

  eBook - ePub

  Electrical Engineering

  Fundamentals

  • Viktor Hacker, Christof Sumereder(Authors)
  • 2020(Publication Date)
  • De Gruyter Oldenbourg

    (Publisher)

  Voltage can cause electric current: If there is a voltage between two particles and these two particles are connected through a conductor, current flows. (More specifically: There is an electric field between the two particles. This field exerts force on the free charge carriers, which causes them to move.)

  Voltage is connected to force: Two particles, with an electric voltage between them, carry a different number of positive and negative electric charges, respectively; therefore, they are positively and negatively charged relative to one another. The respective surplus charges exert forces of attraction on each other.

  Technical generation of voltage:

  • Electric charges are separated by induction (generator, transformer) due to magnetic energy.
  • A chemical reaction separates electric charges in the galvanic cell.
  • Heat separates electric charges in the thermocouple.
  • Radiant energy of the light separates electric charges in the photovoltaic cell (industrially in photovoltaic panels).
  • Pressure separates electric charges in some piezoelectric crystals (e.g. quartz).16

  1.10  Ohm’s law

  Ohm’s law describes a linear correlation in certain electric conductors between voltage drop V and the electric current I which is flowing through the conductors at constant temperature:

  V = R ⋅ I

  V  Voltage in V

  R  Electrical resistance in Ω (Ohm)

  I  Electric current in A

  The resistance R ideally17 is constant, regardless of the magnitude of the current. If this is the case, we talk about linear circuits.

  1.10.1  Resistance R and conductance G

  The resistance

  R  

  of a conductor depends on the material and the spatial dimensions of the conductor. To measure the resistivity of the material, the specific resistance is defined as the resistance of a cube with edges 1 m in length.

  Figure 1.16: Resistance R.

  The unit of resistance is a quantity derived from I and

    V

  . A conductor has a resistance of

  1 Ω

  when a voltage

  V = 1   V

  drives a current of

  I = 1   A

  through the conductor.18

  The technically used resistors can generally be divided into two groups: wire resistors and sheet resistors. The materials of the wire filaments or coatings, usually attached to cylindrical ceramic bodies, have specific resistances with low temperature dependence. The resistance is determined by measuring current and voltage.

  Sign up to read

  Learn more about book
• 

  eBook - ePub

  Circuit Analysis with PSpice

  A Simplified Approach

  • Nassir H. Sabah(Author)
  • 2017(Publication Date)
  • CRC Press

    (Publisher)

  2 Fundamentals of Resistive Circuits

  Objective and Overview

  This chapter introduces (1) the two ideal circuit elements of dc circuits, namely, resistors and sources; (2) the two basic circuit laws, namely, Kirchhoff’s current law (KCL) and Kirchhoff’s voltage law (KVL); and (3) the two basic connections between circuit elements, namely, series and parallel connections.

  The nature of electrical resistance is first explained using a simplified model, following which, the very basic Ohm’s law defining an ideal resistor is presented. Ideal, independent and dependent, voltage and current sources are then discussed, with emphasis on their defining and essential properties.

  Kirchhoff’s laws are introduced as laws derived from conservation of charge and conservation of energy, but which provide a much simpler means of analyzing circuit behavior. Series and parallel connections of circuit elements are then discussed and linked to Kirchhoff’s laws.

  PSpice simulations are introduced in this chapter and are included in all numerical examples, whenever appropriate, to illustrate and verify the results of analytical solutions. This chapter concludes with a very helpful problem-solving approach and illustrating it with examples.

  ⋆ 2.1Nature of Resistance

  Concept: Resistance is fundamentally due to impediments to the movement of current carriers in a conductor under the influence of an applied electric field.

  A sample of a metallic conductor typically consists of a large number of crystals in which the rest positions of the metal atoms at 0 K are arranged in a regular manner that is characteristic of the type of crystal. At temperatures above 0 K, (1) the crystal atoms vibrate, in randomly oriented directions, about their rest positions, with an amplitude of vibration that increases with temperature, and (2) some electrons, referred to as conduction electrons have sufficient energy to detach from their parent atoms and move freely in the crystal, in randomly oriented directions, at thermal velocities of the order of 107

  Sign up to read

  Learn more about book
• 

  eBook - ePub

  Lessons from Nanoelectronics

  A New Perspective on Transport

  • Supriyo Datta(Author)
  • 2012(Publication Date)
  • WSPC

    (Publisher)

  These Lectures, however, are not about the amazing feats of microelectronics or where the field might be headed. They are about a less-appreciated by-product of the microelectronics revolution, namely the deeper understanding of current flow, energy exchange and device

  operation that it has enabled, based on which we have proposed what we call the bottom-up approach. Let me explain what we mean.

  According to Ohm's Law, the resistance R is related to the cross-sectional area A and the length L by the relation

  ρ being a geometry-independent property of the material that the channel is made of.

  The reciprocal of the resistance is the conductance which is written in terms of the reciprocal of the resistivity called the conductivity.

  Our conventional view of electronic motion through a solid is that it is "diffusive," which means that the electron takes a random walk from the source to the drain, traveling in one direction for some length of time before getting scattered into some random direction as sketched in Fig.1.3. The mean free path, λ that an electron travels before getting scattered is typically less than a micrometer (also called a micron = 10-3 mm, denoted µm) in common semiconductors, but it varies widely with temperature and from one material to another.

  Fig.1.3. The length of the channel of an FET has progressively shrunk with every new generation of devices (“Moore’s Law”) and stands today (2010) at ~ 50 nm, which amounts to a few hundred atoms!

  It seems reasonable to ask what would happen if a resistor is shorter than a mean free path so that an electron travels ballistically ("like a bullet") through the channel. Would the resistance still obey Ohm's Law? Would it still make sense to talk about its resistance? These questions have intrigued scientists for a long time, but even twenty five years ago one could only speculate about the answers. Today the answers are quite clear and experimentally well established. Even the transistors in commercial laptops now have channel lengths L

  Sign up to read

  Learn more about book
• 

  eBook - ePub

  Electronics Calculations Data Handbook

  • Daniel McBrearty(Author)
  • 1998(Publication Date)
  • Newnes

    (Publisher)

  Why do some materials conduct electricity, while others don’t? Some materials are populated by good and careful atoms which don’t lose their electrons easily (and probably feel ashamed if they do). Hence the itinerant population is low. The few free electrons that exist tend to sit miserably in one place, having given up hope of ever finding a home. These are insulators, typically air, rubber or the fibreglass backing of a circuit board. In other materials atoms are positively feckless. There are many free electrons and should some charged material come near they move accordingly. How do they know? They feel the voltage. These are conductors. Most metals are conductors. We use copper a great deal, gold where corrosion could be a problem, and sometimes aluminium or other metals for housing equipment.

  Resistance

  Some materials fall into a kind of grey area between being conductors and insulators. We can use these to make resistors. It’s as if the material was a kind of mud; if we make the mud thicker electrons move less easily. The resistance of a given piece of a material depends on ‘how thick the mud is’ (the ‘resistivity’ of the material) and its geometry. Making it thinner increases, and doubling or tripling length doubles or triples, its resistance.

  Ohm’s Law

  The unit for resistance is the ohm, or, and the symbol in equations is R. Now we come to the most important equation in electronics:

  (2.1a)

  with V in volts, I in amps, R in ohms. This is Ohm’s Law. We will use it so much that it bears being rewritten in its two other forms:

  (2.1b)

  and:

  (2.1c)

  These are used so frequently that you need to know them by heart. Ohm’s Law tells us that placing a steady voltage across a material causes a proportional steady current to flow.

  Even insulators and conductors have resistance. Insulators have very high resistance; tens or hundreds of MΩ or more, so that for the normal voltages that we use an unmeasurably small current flows. If the voltage is raised to sufficiently high levels, usually at least a kV, a condition called ‘breakdown’ occurs; electrons are blasted free from atoms within the structure of the material, and its essential nature is changed. You will know if this happens; there is a nasty burning smell, and things stop working. It is a condition which we try to avoid.

  Conductors are the opposite; their resistance is very low, small fractions of an ohm typically. The commonest conductor that we use is copper. We cannot normally measure the voltage across a piece of copper wire, unless it is long. We can find out, from catalogues and so on, the resistance per metre of any given type of wire; this depends on the wire, but figures of around 0.1 Ω/m are typical. Occasionally we need to find this out and calculate the total resistance of a length of cable when our wires are very long, in a large system. The wire will also have a maximum current rating, which is what we can pass through it before the amount of heat generated in it becomes dangerous to its structure. The insulating material around it may melt, causing it to short to things that it shouldn’t, or the conductor itself. We only need know that we should stay comfortably within the maximum rated current for a conductor. In essence, anything can be destroyed with too much voltage/current.

  Sign up to read

  Learn more about book