Name: resistivity in conductors and insulators
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NC K-12 Science Standard Course of Study

9-12

Physical Science

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Motion and Stability- Forces and Interactions

PS.PSc.6.2

Resistivity

התנגדות חשמלית היא תכונה מהותית של חומר, המתארת עד כמה הוא מתנגד לזרימת מטענים.
התנגדות היא יחסי הגומלין של מוליכות חשמלית וניתן להגדירם במונחים של השדה החשמלי וצפיפות הזרם. יחידת SI של התנגדות היא אוהם-מטר.
למוליכים טובים יש מוליכות גבוהה אך התנגדות נמוכה, בעוד שלמבודדים טובים יש מוליכות נמוכה אך התנגדות גבוהה.
הטמפרטורה משפיעה על ההתנגדות של חומרים מסוימים. בחומרים רבים, התלות היא ליניארית בקירוב וניתן למדל אותה באמצעות משוואה ליניארית כאשר ρ הוא ההתנגדות של החומר בטמפרטורה, α הוא מקדם הטמפרטורה של החומר ו-ρ0 הוא ההתנגדות בטמפרטורת החדר.
ההתנגדות של חומרים מסוימים, כגון נחושת, עולה ככל שהטמפרטורה עולה; באחרים, כמו פחמן, ההתנגדות פוחתת ככל שהטמפרטורה עולה.
במוליכים למחצה, מקדם הטמפרטורה שלילי, מה שמרמז על כך שההתנגדות פוחתת ככל שהטמפרטורה עולה.

<ol>
	<li>OpenStax. (2019). פיזיקה אוניברסיטאית כרך 2. [גרסת אינטרנט], עמ' 396 - 398. מקור: <a href="https://openstax.org/books/university-physics-volume-2/pages/9-3-resistivity-and-resistance">https://openstax.org/books/university-physics-volume-2/pages/9-3-resistivity-and-resistance</a></li>
</ol>

התנגדות סגולית

<div style="direction:rtl">

 כאשר מופעל מתח על מוליך, נוצר שדה חשמלי, ומטענים במוליך מרגישים את הכוח הנובע מהשדה החשמלי. צפיפות הזרם שנוצרת תלויה בשדה החשמלי ובתכונות החומר. בחומרים מסוימים, כולל מתכות בטמפרטורה נתונה, צפיפות הזרם פרופורציונלית בערך לשדה החשמלי. במקרים אלה, ניתן לעצב את צפיפות הזרם כ: 

 <img alt="Equation1" src="/files/ftp_upload/13746/13746_Equation_1.svg" style="text-align: center; height: 16px;"> 

 כאשר σ היא המוליכות החשמלית ומיוצגת על ידי (Ω·m)−1. מוליכות חשמלית מקבילה למוליכות תרמית והיא מדד ליכולת של חומר להוליך או להעביר חשמל. מוליכים יש מוליכות חשמלית גבוהה יותר מאשר מבודדים. מוליכות היא תכונה מהותית של חומר. תכונה מהותית נוספת של חומר היא ההתנגדות שלו, או ההתנגדות החשמלית. ההתנגדות של חומר היא מדד למידת ההתנגדות של החומר לזרימת הזרם החשמלי. ניתן להגדיר התנגדות כהדדית של מוליכות חשמלית והיא מיוצגת על ידי האות היוונית rho, ρ. יחידת ההתנגדות ביחידות SI היא מד אוהם. ניתן להגדיר התנגדות גם כיחס בין השדה החשמלי לצפיפות הזרם. ככל שההתנגדות גדולה יותר, כך השדה הדרוש לייצור צפיפות זרם נתונה גדול יותר. ככל שההתנגדות נמוכה יותר, כך צפיפות הזרם המופקת על ידי שדה חשמלי נתון גדולה יותר. כפי שמופיע בטבלה 1, טוב  מוליכים מראים מוליכות גבוהה והתנגדות נמוכה, ואילו מבודדים טובים מראים מוליכות נמוכה והתנגדות גבוהה.

 טבלה 1: מפרטת ערכי התנגדות ומוליכות עבור חומרים שונים. 
 <table style="margin-left: auto; margin-right: auto;"> 
 <tbody style="border: 1px solid black;"> 

 <tr> 
 <td style="color: black; border: 1px solid black; text-align: center;">Materials</td> 
 <td style="color: black; border: 1px solid black; text-align: center;">Conductivity, σ ( Ω · m)−1</td> 
 <td style="color: black; border: 1px solid black; text-align: center;">Resistivity, ρ ( Ω · m)</td> 
 <td style="color: black; border: 1px solid black; text-align: center;">Temperature Coefficient, α (°C)−1</td> 
 </tr> 

 <tr> 
 <td style="color: black; border: 1px solid black; text-align: center;">Silver</td> 
 <td style="color: black; border: 1px solid black; text-align: center;">6.29 × 107</td> 
 <td style="color: black; border: 1px solid black; text-align: center;">1.59 × 10−8</td> 
 <td style="color: black; border: 1px solid black; text-align: center;">0.0038</td> 
 </tr> 
 <tr> 
 <td style="color: black; border: 1px solid black; text-align: center;">Copper</td> 
 <td style="color: black; border: 1px solid black; text-align: center;">5.95 × 107</td> 
 <td style="color: black; border: 1px solid black; text-align: center;">1.68 × 10−8</td> 
 <td style="color: black; border: 1px solid black; text-align: center;">0.0039</td> 
 </tr> 
 <tr> 
 <td style="color: black; border: 1px solid black; text-align: center;">Gold</td> 
 <td style="color: black; border: 1px solid black; text-align: center;">4.10 × 107</td> 
 <td style="color: black; border: 1px solid black; text-align: center;">2.44 × 10−8</td> 
 <td style="color: black; border: 1px solid black; text-align: center;">0.0034</td> 
 </tr> 
 <tr> 
 <td style="color: black; border: 1px solid black; text-align: center;">Aluminum</td> 
 <td style="color: black; border: 1px solid black; text-align: center;">3.77 × 107</td> 
 <td style="color: black; border: 1px solid black; text-align: center;">2.65 × 10−8</td> 
 <td style="color: black; border: 1px solid black; text-align: center;">0.0039</td> 
 </tr> 
 <tr> 
 <td style="color: black; border: 1px solid black; text-align: center;">Tungsten</td> 
 <td style="color: black; border: 1px solid black; text-align: center;">1.79 × 107</td> 
 <td style="color: black; border: 1px solid black; text-align: center;">5.60 × 10−8</td> 
 <td style="color: black; border: 1px solid black; text-align: center;">0.0045</td> 
 </tr> 
 <tr> 
 <td style="color: black; border: 1px solid black; text-align: center;">Carbon (pure)</td> 
 <td style="color: black; border: 1px solid black; text-align: center;">2.86 × 10−6 </td> 
 <td style="color: black; border: 1px solid black; text-align: center;">3.50 × 10−5 </td> 
 <td style="color: black; border: 1px solid black; text-align: center;">−0.0005</td> 
 </tr> 
 <tr> 
 <td style="color: black; border: 1px solid black; text-align: center;">Silicon</td> 
 <td style="color: black; border: 1px solid black; text-align: center;"></td> 
 <td style="color: black; border: 1px solid black; text-align: center;"> 0.1 − 2300</td> 
 <td style="color: black; border: 1px solid black; text-align: center;">−0.07</td> 
 </tr> 
 <tr> 
 <td style="color: black; border: 1px solid black; text-align: center;">Amber</td> 
 <td style="color: black; border: 1px solid black; text-align: center;">2.00 × 10−15 </td> 
 <td style="color: black; border: 1px solid black; text-align: center;">5 × 1014</td> 
 <td style="color: black; border: 1px solid black; text-align: center;"></td> 
 </tr> 
 <tr> 
 <td style="color: black; border: 1px solid black; text-align: center;">Glass</td> 
 <td style="color: black; border: 1px solid black; text-align: center;">10−9 − 10−14</td> 
 <td style="color: black; border: 1px solid black; text-align: center;">109 − 1014</td> 
 <td style="color: black; border: 1px solid black; text-align: center;"></td> 
 </tr> 
 <tr> 
 <td style="color: black; border: 1px solid black; text-align: center;">Lucite</td> 
 <td style="color: black; border: 1px solid black; text-align: center;"><10−13 </td> 
 <td style="color: black; border: 1px solid black; text-align: center;">>1013</td> 
 <td style="color: black; border: 1px solid black; text-align: center;"></td> 
 </tr> 
 </tbody> 
 </table>
 </div>

כאשר מופעל מתח על מוליך, נוצר שדה חשמלי, ומטענים במוליך מרגישים את הכוח הנובע מהשדה החשמלי. ה...

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Current and Resistance

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KEY TERMS AND CONCEPTS

מונחים ומושגים מרכזיים

resistivity in conductors and insulators

Resistivity describes how much a material opposes electric current. When a voltage is applied to a conductor, an electric field forms. The charges in the conductor feel that force, and a current density develops. In some materials, including metals at a given temperature, the current density is approximately proportional to the electric field.

In those cases, current density can be modeled with conductivity, written as sigma. Electrical conductivity is measured in (ohm·m)^−1. It tells how well a material can conduct electricity. This idea is similar to thermal conductivity, which describes how well a material carries heat. Conductors have higher electrical conductivity than insulators, and conductivity is an intrinsic property of the material.

Resistivity, written as rho, is another intrinsic property. It is the reciprocal of electrical conductivity. In SI units, resistivity is measured in ohm-meter. It can also be defined as the ratio of electric field to current density. A higher resistivity means a larger electric field is needed to produce a given current density. A lower resistivity means the same electric field produces a larger current density.

The transcript also compares common materials. Good conductors have high conductivity and low resistivity. Good insulators have low conductivity and high resistivity. Examples of good conductors include silver, copper, gold, aluminum, and tungsten. Pure carbon has much lower conductivity than these metals. Silicon falls between conductor and insulator values, while amber, glass, and Lucite show very high resistivity and very low conductivity.

Resistivity in Conductors and Insulators

electrical current

Current Flow in Simple Circuits

Electrical current is the flow of charge in a circuit. A large current means a large amount of charge moves through a wire in a short time. A small current means only a small amount of charge moves through the circuit over a longer time. Examples include the current needed to run a refrigerator and the smaller current used by a handheld calculator. The SI unit for current is the ampere, or amp. It is named for the French physicist André-Marie Ampère (1775–1836). One ampere means one coulomb of...

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Electrical current in a conductor depends on moving charges and the tiny drift speed of those charges. When a free charge enters a wire, it pushes nearby charges ahead because like charges repel each other. That push spreads through the material very quickly, so the electrical signal moves through the system at nearly the speed of light. This fast signal is not the same as the slow motion of each charge. It is a rapidly spreading change in the electric field, often described as an electrical...

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Current Density in Wires and Solutions

Current density describes how much electric current passes through a given cross-sectional area. It helps show not just the size of the current, but also how it is distributed through a conductor. The current density can change from point to point because the local charge flow can vary. If the current flow is uniform, the amount of current is the same at every point along the conductor, even when the conductor’s area changes. Current density is measured in amperes per square meter. Its...

resistivity

Resistivity describes how much a material opposes electric current. When a voltage is applied to a conductor, an electric field forms. The charges in the conductor feel that force, and a current density develops. In some materials, including metals at a given temperature, the current density is approximately proportional to the electric field. In those cases, current density can be modeled with conductivity, written as sigma. Electrical conductivity is measured in (ohm·m)^−1. It tells how well...

resistance

Factors That Affect Electrical Resistance

Electrical resistance describes how much a conductor opposes the flow of current. It is represented by R. When current passes through a conductor, heat is also produced. Resistance is tied to the material’s resistivity, which is a property of the material used to make an electrical component. Resistance is different from resistivity. Resistivity belongs to the material itself, while resistance belongs to the finished component. To study this relationship, consider a wire with length L,...

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Measuring Current, Voltage, and Resistance

Ohm's law describes the relationship between current, voltage, and resistance in many materials. In these cases, the current through a substance is directly proportional to the voltage applied to it. The idea was first shown experimentally by German physicist Georg Simon Ohm, who studied current in a metal wire. A material, component, or device that follows this pattern is called ohmic. An ohmic component has a current that increases in step with voltage. A material or component that does not...

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A diode is a nonohmic circuit element that makes current and voltage behave differently from Ohm’s law. In most substances, current is proportional to the voltage applied, but a diode does not show a linear current-voltage relationship. A diode is a semiconducting device with two terminals: an anode, which is the positive terminal, and a cathode, which is the negative terminal. It allows current to flow in only one direction. In a simple circuit with a battery, a diode, and a resistor, the...

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Electrical power in a circuit depends on current and voltage. It is the product of these two values and is measured in watts, or joules per second. That relationship helps explain how much energy a circuit can deliver. A car’s auxiliary power outlet is one real-world example. Some outlets are rated at 20 amps and 12 volts, so they can deliver a maximum of 240 watts. That rating shows the upper limit of power the circuit can provide to devices such as a cell phone charger. Bulb wattage also...

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Charge conservation and current flow are linked through the continuity equation. The current density is the amount of current flowing per unit cross-sectional area. The current through a surface can be written as a surface integral of the current density. The conservation of charge says that the total current leaving a volume equals the rate at which charge inside that volume decreases. The total charge can be written using volume charge density, which is a space function. Because of this, the...

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Current density at a boundary changes when two conducting materials have different electrical conductivities. The normal component of current density stays continuous across the interface. The tangential component, which runs along the surface, becomes discontinuous across the boundary. Consider two conducting media with conductivities σ1 and σ2 separated by an interface. At point P1 in medium 1, the steady current density makes an angle α1 with the normal. At point P2 in medium 2, the current...

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Resistance and Ohm's Law in Conductors

Resistance and Ohm's law help explain how electric current moves through a conductor. In a perfect conductor, the electric field inside is zero because free electrons move to cancel it. Any extra charge then stays on the surface. In a practical conductor, an applied electric field can remain in place. That field drives electrons through the material and creates a current. The current density, which is current per unit area, is related to the electric field. More generally, it is related to the...

theory of metallic conduction

Electron Drift in Metallic Conduction

Electron drift in metallic conduction explains how free electrons move through a conductor. A classical model can describe this motion closely, even though quantum mechanics gives the best overall picture. This model is called the theory of metallic conduction. In this theory, Newton's second law is used to find the acceleration of an electron when an electric field is applied. The electron's velocity is then found from that acceleration. The electron travels through a crystal of positive ions...

key terms and concepts

Learn how resistivity relates to conductivity, electric fields, and current density. See why conductors and insulators behave differently in common materials.

Resistivity in Conductors and Insulators | JoVE K12

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JoVE Core Physics introduces the theory and application of fundamental physics topics, including kinematics, dynamics, fluid mechanics, statics, waves, and acoustics, with concise and easy-to-understand animated videos. Additionally, the scientist-in-action videos demonstrate the application of related concepts in classical and original research experiments performed in today's laboratories worldwide.

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Non-ohmic Devices

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Construct an explanation to compare simple series and parallel circuits in terms of Ohm's Law.

Continuity Equation

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Boundary Conditions for Current Density

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PS.PSc.6.4

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Resistivity in Conductors and Insulators

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