Tag Archives: resistivity
Solutions: Resistance of a Wire WS
Resistance of a Wire
Resistance
Electrical charges can move easily in some materials (conductors) and less freely in others (insulators), as we learned previously. We describe a material’s ability to conduct electric charge as conductivity. Good conductors have high conductivities. The conductivity of a material depends on:
- Density of free charges available to move
- Mobility of those free charges
In similar fashion, we describe a material’s ability to resist the movement of electric charge using resistivity, symbolized with the Greek letter rho (
). Resistivity is measured in ohm-meters, which are represented by the Greek letter omega multiplied by meters (
•m). Both conductivity and resistivity are properties of a material.
When an object is created out of a material, the material’s tendency to conduct electricity, or conductance, depends on the material’s conductivity as well as the material’s shape. For example, a hollow cylindrical pipe has a higher conductivity of water than a cylindrical pipe filled with cotton. However, shape of the pipe also plays a role. A very thick but short pipe can conduct lots of water, yet a very narrow, very long pipe can’t conduct as much water. Both geometry of the object and the object’s composition influence its conductance.
Focusing on an object’s ability to resist the flow of electrical charge, we find that objects made of high resistivity materials tend to impede electrical current flow and have a high resistance. Further, materials shaped into long, thin objects also increase an object’s electrical resistance. Finally, objects typically exhibit higher resistivities at higher temperatures. We take all of these factors together to describe an object’s resistance to the flow of electrical charge. Resistance is a functional property of an object that describes the object’s ability to impede the flow of charge through it. Units of resistance are ohms ().
For any given temperature, we can calculate an object’s electrical resistance, in ohms, using the following formula, which can be found on your reference table.
In this formula, R is the resistance of the object, in ohms (), rho () is the resistivity of the material the object is made out of, in ohm*meters (•m), L is the length of the object, in meters, and A is the cross-sectional area of the object, in meters squared. Note that a table of material resistivities for a constant temperature is given to you on the reference table!
Let’s try a sample problem calculating the electrical resistance of an object:
Question: A 3.50-meter length of wire with a cross-sectional
area of 3.14 × 10–6 m2 at 20° Celsius has a resistance of 0.0625Answer:
Introduction to Current Electricity
Flow of Charge
Electric current is the flow of charge, much like water currents are the flow of water molecules. Water molecules tend to flow from areas of high gravitational potential energy to low gravitational potential energy. Electric currents flow from high electric potential to low electric potential. And the greater the difference between the high and low potential, the more current that flows!
In a majority of electric currents, the moving charges are negative electrons. However, due to historical reasons dating back to Ben Franklin, we say that conventional current flows in the direction positive charges would move. Although inconvenient, it’s fairly easy to keep straight if you just remember that the actual moving charges, the electrons, flow in a direction opposite that of the electric current. With this in mind, we can state that positive current flows from high potential to low potential, even though the charge carriers (electrons) actually flow from low to high potential.
Electric current (I) is measured in amperes (A), or amps, and can be calculated by finding the total amount of charge (
q), in Coulombs, which passes a specific point in a given time (t). Electric current can therefore be calculated as:
Question: A charge of 30 Coulombs passes through a 24-ohm resistor in 6.0 seconds. What is the current through the resistor?
Answer:
Resistance
Electrical charges can move easily in some materials (conductors) and less freely in others (insulators), as we learned previously. We describe a material’s ability to conduct electric charge as conductivity. Good conductors have high conductivities. In similar fashion, we describe a material’s ability to resist the movement of electric charge using resistivity, symbolized with the Greek letter rho (). Resistivity is measured in ohm-meters, which are represented by the Greek letter omega multiplied by meters (•m). Both conductivity and resistivity are properties of a material.
Ball Lightning Sample:
Introduction to Electrostatics
Building Blocks of Matter
Matter is made up of atoms. Once thought to be the smallest building blocks of matter, we now know that atoms can be broken up into even smaller pieces, known as protons, electrons, and neutrons. Each atom consists of a dense core of positively charged protons and uncharged (neutral) neutrons. This core is known as the nucleus. It is surrounded by a “cloud” of much smaller, negatively charged electrons. These electrons orbit the nucleus in distinct energy levels. To move to a higher energy level, an electron must absorb energy. When an electron falls to a lower energy level, it gives off energy.
Most atoms are neutral — that is, they have an equal number of positive and negative charges, giving a net charge of 0. For this to occur, the number of protons must equal the number of electrons. In certain situations, however, an atom may gain or lose electrons. In these cases, the atom as a whole is no longer neutral, and we call it an ion. If an atom loses one or more electrons, it has a net positive charge, and is known as a positive ion. If, instead, an atom gains one or more electrons, it has a net negative charge, and is therefore called a negative ion. Like charges repel each other, while opposite charges attract each other. In physics, we represent the charge on an object with the symbol q.
Charge is a fundamental measurement in physics, much as length, time, and mass are fundamental measurements. The fundamental unit of charge is the Coulomb [C], which is a very large amount of charge. Compare that to the magnitude of charge on a single proton or electron, known as an elementary charge, which is equal to 1.6*10^-19 coulomb. It would take 6.25*10^18 elementary charges to make up a single coulomb of charge! (Don’t worry about memorizing these values, they’re listed for you on the front of the reference table!).
Question: An object possessing an excess of 6.0*10^6 electrons has what net charge?
Answer:
Conductors and Insulators
Certain materials allow electric charges to move freely. These are called conductors. Examples of good conductors include metals such as gold, copper, silver, and aluminum. In contrast, materials in which electric charges cannot move freely are known as insulators. Good insulators include materials such as glass, plastic, and rubber.
Conductors and insulators are characterized by their resistivity, or ability to resist movement of charge. Materials with high resistivities are good insulators. Materials with low resistivities are good conductors.
Semiconductors are materials which, in pure form, are good insulators. However, by adding small amounts of impurities known as dopants, their resistivities can be lowered significantly until they become good conductors.
Charging by Conduction
Materials can be charged by contact, or conduction. If you take a balloon and rub it against your hair, some of the electrons from the atoms in your hair are transferred to the balloon. The balloon now has extra electrons, and therefore has a net negative charge. Your hair has a deficiency of electrons, therefore it now has a net positive charge.
Much like momentum and energy, charge is also conserved. Continuing our hair and balloon example, the magnitude of the net positive charge on your hair is equal to the magnitude of the net negative charge on the balloon. The total charge of the hair/balloon system remains zero (neutral). For every extra electron (negative charge) on the balloon, there is a corresponding missing electron (positive charge) in your hair. This known as the law of conservation of charge.
Conductors can also be charged by contact. If a charged conductor is brought into conduct with an identical neutral conductor, the net charge will be shared across the two conductors.
Question: If a conductor carrying a net charge of 8 elementary charges is brought into contact with an identical conductor with no net charge, what will be the charge on each conductor after they are separated?
Answer: Each conductor will have a charge of 4 elementary charges.
Question: What is the net charge (in coulombs) on each conductor after they are separated?
Answer:
Coulomb’s Law
We know that like charges repel, and opposite charges attract. In order for charges to repel or attract, they apply a force upon each either. Similar to the manner in which the force of attraction between two masses is determined by the amount of mass and the distance between the masses, as described by Newton’s Law of Universal Gravitation, the force of attraction or repulsion is determined by the amount of charge and the distance between the charges. The magnitude of the electrostatic force is described by Coulomb’s Law.
Coulomb’s Law states that the magnitude of the electrostatic force (Fe) between two objects is equal to a constant, k, multiplied by each of the two charges, q1 and q2, and divided by the square of the distance between the charges (r2). The constant k is known as the electrostatic constant, and is given on the reference table as: 
.
Notice how similar this formula is to the formula for the gravitational force! Both Newton’s Law of Universal Gravitation and Coulomb’s Law follow the inverse-square relationship, a pattern that repeats many times over in physics. The further you get from the charges, the weaker the electrostatic force. If you were to double the distance from a charge, you would quarter the electrostatic force on a charge.
Formally, a positive value for the electrostatic force indicates that the force is a repelling force, while a negative value for the electrostatic force indicates that the force is an attractive force. Because force is a vector, you must assign a direction to it. To determine the direction of the force vector, once you have calculated its magnitude, use common sense to tell you the direction on each charged object. If the objects have opposite charges, they are being attracted, and if they have like charges, they must be repelling each other.
Question: Three protons are separated from a single electron by a distance of 1*10^-6 m. Find the electrostatic force between them. Is this force attractive or repulsive?
Answer:
