Chapter 18 Electric Currents
Electric Current Current Equation What is the current units?
(Circuit Diagram in Picture) More precisely, the electric current in a wire is defined as the net amount of charge that passes through the wires full cross section at any point per unit time. Thus, the current I is defined as I = Delta Q/Delta t Where I is current, Delta Q is the amount of charge that passes through the conductor at any location during the time interval delta t. Electric current is measured in colulombs per second, given for the name ampere or amp or A. 1 A = 1 C/s.
Resistor Color Code example
(No need to memorize but look at the diagram on page 507) First two colors represent the first two digits. The third color represents the power of ten that its multiplied by. The fourth color is the manufactured tolerance.
Clarifications regarding batteries
- Batteries maintain a nearly constant potential difference, but the current varies - Resistance is a property of a material or device. - Current is not a vector, but it does have a direction. - Current and Charge don't get used up. Whatever charges goes in one end of a circuit comes out the other end. But the current through a device might respond to voltage or resistance increases or decreases, as of I = V/R
Summary of Chapter 18 Quick
1. A battery is a constant source of constant potential difference. 2. Electric current is the rate of flow of electric charge: I = Q/t 3. Conventional current is in the direction that a positive charge would flow. 4. Resistance is the ratio of voltage to current: V = IR, R = V/I 5. Ohmic materials have constant resistance, independent of voltage. 6. Resistance is determined by shape and material: R = p* l/A (p is resistivity coefficient, l is length, and A is cross sectional area) 7. Power in an electric circuit: P =IV 8. Power related to ohms law: P = I^2* R, P = V^2/R 9. Direct current is constant 10. Alternating current varies sinusoidally: I = V/R = V0/R * sin ω*t = I0 *sinω*t 11. The average (rms) current and voltage: I rms = Square Root of I^2 (with line over it) = I0/ Square root of 2 = 0.707 I0 V rms = Square Root of V^2 (with line over it) = V0/ Square root of 2 = 0.707 V0 P(line over it) = I rms * V rms
What does a battery produce? What are the simplest forms of batteries?
A battery produces electricity by transforming chemical energy into electrical energy. Theres a variety of electric cells and batteries now from flashlight batteries to the storage battery of a car. The simplest batteries contain two plates or rods made of dissimilar metals (one can be carbon) called electrodes. The electrodes are immerse in a solution or paste, such as a dilute acid, called the electrolyte. Such a device is properly called an electric cell, and several cells connected together is a battery, although today even a single cell is called a battery. The chemical reactions involved in most electric cells are quite complicated.
Complete and Open circuits
A current can flow in a circuit only if there is a continuous conducting path. Which in that case, we then have a complete circuit. If there is a break in the circuit, like a cut wire, its an open circuit and no current flows. In any single circuit, with only a single path for current to follow, a steady current at any instant is the same at on point as at any other point. This follows from the conservation of electric charge as charge doesn't disappear. A battery does not create or destroy any net charge, nor does a lightbulb absorb or destroy charge.
Electric devices and Resistance to flow of current
All electric devices, from heaters to lightbulbs to stereo amplifiers, offer resistance to the flow of current. The filaments of lightbulbs and electric heaters are special types of wires whose resistance results in their becoming very hot. Generally, the connecting wires have very low resistance in comparison to the resistance of the wire filaments or coils, so the connecting wires usually have a minimal effect on the magnitude of the current.
Potential or Voltage Drop
An electric potential decrease, as from point A to point B in the previous example, is often called a potential drop or voltage drop.
Average Power equations
Because the current is squared, we see that the power is always positive. The quantity sin^2ω*t varies between - and 1, and its not too difficult to show that its average value is 1/2. Thus the average power transformed, P(with line over it), is P(with line over it), = 1/2 * I^20 * R Since power can also be written P = V^2/R = (V^20/R)(sinω)*t, we also have that the average power is: P(with line over it) = 1/2 V^20/R The average or mean value of the square of the current or voltage is thus important for calculating average power: I^2 (with line over it) = 1/2* I0^2 and V^2(with line over it) = 1/2* V0^2. The square root of each of these is the rms or root-mean-square value of the current or voltage: I rms = Square Root of I^2 (with line over it) = I0/ Square root of 2 = 0.707 I0 V rms = Square Root of V^2 (with line over it) = V0/ Square root of 2 = 0.707 V0 The rms values of V and I are sometimes called effective values. They are useful because they can be substituted directly into the power formulas. P(line over it) = I^2 rms * R = 1/2*I0^2*R P(line over it) = V^2 rms/R = 1/2*V0^2/R P(line over it) = I rms * V rms
In electostatic situations, what are the conditions of the electric field? What needs to occur when charges are moving?
Beforehand, in electrostatic situations, the electric field must be zero inside a conductor because if it weren't the charges would move. But when charges are moving along a conductor, an electric field is needed to set charges into motion, and to keep them in motion against even low resistance in any normal conductor. We can control the flow of charge using electric fields and electric potential (voltage). In order to have a current in a wire, a potential difference is needed, which can be provided by a battery.
What occurs if a continuous conducting wire is connected to the terminals of a battery?
Conductors contain many free electrons. Thus if a continuous conducting wire is connected to the terminals of a battery, negatively charged electrons flow through the wire. When the wire is first connected, the potential difference between the terminals of the battery sets up an electric field inside the wire and parallel to it. Free electrons at one end of the wire are attracted into the positive terminal, and at the same time other electrons enter the other end of the positive terminal, and at the same time other electrons enter the other end of the wire at the negative terminal of the battery. There is a continuous flow of electrons throughout the wire that begins as soon as the wire is connected to both terminals.
Electric Power
Electric energies value is that it can be easily transformed into other forms of energy. In other devices like electric heaters, stoves, etc, electric energy is transformed into thermal energy in a wire resistance known as heating element. In ordinary lightbulbs, the tiny wire filament becomes so hot it glows, only a few percent of the energy is transformed into visible light, and the rest, over 90% into thermal energy. Lightbulb filaments and heating elements in household appliances have resistances typically of a few ohms to a few hundred ohms. Electric energy is transformed into thermal energy or light in such devices, and there are many collisions between the moving electrons and the atoms of the wire. In each collision, part of the electrons kinetic energy is transferred to the atom with which it collides. As a result, the kinetic energy of the wires atoms increases and hence the temp of the wire element increases. The increased thermal energy can be transferred as heat by conduction and convection to the air in a heater or to food in a pan, by radiation to bread in a toaster, or radiated as light.
Electrical Resistance and Ohms Law What is an Ohm?
Electron flow is impeded because of collisions with the atoms of the wire. We define electrical resistance R as the proportionality factor between the voltage V(between the ends of the wire) and the current I (passing through the wire): V = I* R R is a constant independent of V, and this is all knwon as Ohm's Law. But they only apply to materials or devices for which R is a constant independent of V. But R is not a constant for many substances other than metals nor for devices like diodes, vacuum tubes, transistors, and so on. Even for metals, R is not constant if the temperature changes much: for a lightbulb filament the measured resistance is low for small currents, but is much higher at the filaments normal large operating current that puts it at the high temp needed to make it glow. Thus Ohm's 'Law' is not a fundamental law of nature, but rather a description of a certain class of materials: metal conductors, whose temperature does not change much. Such materials are said to be ohmic, but materials who don't follow this are said to be nonohmic. Most of the time questions will state if they are nonohmic. The unit for resistance is called the ohm and is abbreviated by omega symbol. And because R = V/I, we see that 1Ω = 1 V/A
What does how large the current is in a wire depend on?
Exactly how large the current is in a wire depends not only on the voltage between its ends but also on the resistance the wire offers to the flow of electrons.
Simple electric cell
For example, if you use sulfuric acid solution as the electrolyte, one of the electrodes can be carbon and the other zinc. The part of each electrode outside the solutio nis called the terminal, and the connections to wire sand circuits are made here. The acid tends to dissolve the zinc electrode. Each zinc atom leaves two electrons behind on the electrode and enters the solution as a positive ion. The zinc electrode thus acquires a negative charge. The electrolyte becomes positively charged and can pull electrons off the carbon electrode. Thus the carbon electrode becomes positively charged. Because there is an opposite charge on the two electrodes, there is a potential difference between the two terminals.
How are household circuits designed?
Household circuits are designed with the various devices connected so that each receives the standard voltage from the electric company, typically 120 V in USA. Circuits with the devices arranged as is the picture on page 513 are called parallel circuits. When a fuse blows or circuit breaker opens, it's important to check the total current being drawn on that circuit, which is the sum of the currents in each device.
Describe a cell whose terminals are not connected
In a cell with terminals not connected, only a small amount of zinc is dissolved, for as the zinc electrode becomes increasingly negative, any new positive zinc ions produced are attracted back to the electrode. Thus, a particular potential difference or voltage is maintained between the two terminals. If charge is allowed to flow between the terminals, say through a wire or lightbulb, then more zinc can be dissolved. After a time, one or the other electrode is used up and the cell becomes dead.
Resistors
In many circuits, particularly electronic devices, resistors are used to control the amount of current. Resistors have resistances ranging from less than an ohm to millions of ohms. The main types are wire wound resistors which consist of a coil of fine wire, 'composition' resistors which are usually made of carbon, resistors made of thin carbon or metal films, and (on tiny integrated circuit chips) undoped semiconductors. When drawing diagrams of circuits, use the picture to indicate a resistance. Wires whose resistance is negligible, however, are shown simply as straight lines.
Real circuits with ground conductor.
In many real circuits, wires are connected to a common conductor that provides continuit. This common conductor is called ground, usually represented by ⏚, and really is connected to the ground for a building or house. In a car, one terminal of the battery is called ground, but is not connected to the earth itself, its connected to the frame of the car, as is one connection to each lightbulb and other devices. Thus the car frame is a conductor in each circuit, ensuring a continuous path for charge flow, and is called ground for the cars circuits.
Resistivity Give examples of resistivity coefficients
Its found experimentally that the resistance R of a uniform wire is directly proportional to its length l and inversely proportional to its cross sectional area A. That is: R = p* l/A where p, the constant of proportionality, is called the resistivity and depends on the material used. Typical values of p, whose units are Ω * m. There are categories of conductors, insulators, and semiconductors. The values depend somewhat on purity, heat treatment, temperature, and other factors. For example, silver has the lowest resistivity and is thus the best conductor, but its expensive. Copper is close and much less expensive, which is why most wires are made of copper. Aluminum, although it has a higher resistivity, is much less dense than cooper, thus its preferable to copper in some situations such as for transmission lines, because its resistance for the same weight is less than that for copper. For ex: silver is 1.59 * 10^-8 and Copper is 1.68 * 10^-8
Power for Ohmic Devices(slides)
P = IV P = I^2 * R P = V^2/R
If you have a current entering a resistor, with point A on the left side of the resistor and point B on the right side of the resistor, is the potential higher at point A or B? Is the current greater at point A or at point B?
Positive charge always flows from + to -, from high to low potential. So if current I is conventional positive current, then point A is at a higher potential than point B. Conservation of charge requires whatever charge flows into the resistor at point A, an equal amount of charge emerges at point B. Charge or current doesn't get used up by a resistor. So the current is the same at A and B.
Relation of Power and Resistance with alternating currents
The current is considered positive when the electrons flow in one direction and negative when they flow in the opposite direction. Thus an alternating current is as positive as it is negative. Thus the average current is zero. This does not mean, however, that no power is needed or no heat is produced in a resistor. Electrons do move back and forth and do produce heat. The power transformed in a resistance R at any instant is: P = I^2R = I0^2* R* sin^2ω*t
Power in Household Circuits: Fuses/Circuit Breakers
The electric wires that carry electricity to lights and other electric appliances in houses and buildings have some resistance, although usually it's quite small. Nonetheless, if the current is large enough, the wires will heat up and produce thermal energy at a rate equal to I^2* R, where R is the wires resistance. One possible hazard is that the current carrying wires in the wall of a building may become so hot as to start a fire. Thicker wires have less resistance and thus can carry more current without becoming too hot. When a wire carries more current than is safe, it's said to be overloaded. To prevent overloading, fuses or circuit breakers are installed in circuits. They are basically switches taht open the circuit when the current exceeds a safe value. A 20 A fuse or curcuit breaker for examples, opens when the current passing through it exceeds 20 A. If a circuit repeatedly burns out a fuse or opens a circuit breaker, and no connected device requires more than 20 A, there are two possibilities: there may be too many devices drawing current in that circuit, or there is a fault somewhere, such as a 'short'. A short or 'short circuit' means that two wires have touched that should not have, perhaps because the insulation has worn through, so the path of the current is shortened through a path of very low resistance. With reduced resistance, the current becomes very large and can make a wire hot enough to start a fire. Short circuits should be remedied immediately.
Purpose of the Battery
The purpose of a battery is to produce a potential difference, which can then make charges move. When a continuous conducting path is connected between the terminals of a battery, we have an electric circuit. We use the symbol in the picture to represent a battery. The device connected to the battery could be a lightbulb, heater, a radio, or some other device. When such a circuit is formed, charge can move or flow through the wires of the circuit, from one terminal of the battery to the other, as long as the conducting path is continuous. Any flow of charge such as this is called an electric current.
Temperature dependence of resistivity
The resistivity of a material depends somewhat on temp. The resistance of metals generally increases of temperature. This isn't surprising because at higher temps the atoms are moving more rapidly and are arranged in a less orderly fashion. This leads to our temperature coefficients of resistivity Not that important
Source of Electricity discovered by Volta
The source of electricity was not in the animal itself, but rather in the contact between dissimilar metals. A moist conductor at the contact point of two dissimilar metals was also necessary in the circuit to be effective.
Peak Voltage Equations
The voltage produced by an ac electric generator is sinusoidal. The current it produces is thus sinusoidal. We can write the voltage as a function of time as: V = V0 sin(2pi*f)*t = V0 * sinω t The potential V oscillates between +V0 and -V0, and V0 is referred to as the peak voltage. The frequency f is the numbe rof complete oscillations per second and ω = 2pi*f. f is typically 60 Hz but many countries also use 50 Hz.
Voltage between terminals of the battery What occurs when two or more cells are connected
The voltage that exists between the terminals of a battery depends on what the electrodes are made of and their relative ability to be dissolved or give up electrons. When two or more cells are connected so that the positive terminal of one is connected to the negative terminal of the next, they are said to be connected in series and their voltages add up.
Do wires/conductors have the highest resistance at what lengths and cross sectional areas?
Their highest resistance would be at longest lengths and smaller cross sectional areas. But their least would be at the most area and least lengths.
Finding Power Transformed by an Electric Device The Watt as well conversion to kilowatt hour
To find the power transformed by an electric device, recall that the energy transformed when a charge Q moves through a potential difference V is QV. Then the power P, which is the rate energy is transformed is: P = energy transformed/ time = QV / t The charge that flows per second, Q/t is also equal to the electric current. Thus we can alter the equation to: P = I * V This general relation gives us the power transformed by any device where P is power, I is current passing through, and V is potential difference across it. It also gives the power delivered by a source such as a battery. The SI unit of electric power is the same as for any kind of power, the watt (1 W = 1 J/s). The rate of energy transformation in a resistance R can be written in two other ways, starting with the general relation P = IV, and substituting in Ohms Law, V = IR. P = IV = I(IR) = I^2 * R because V = I * R via ohms law and P = IV = (V/R) *V = V^2/R since if we rearrange ohms law, I = V/R. But these two equations only apply to resistors, whereas P= IV is more general and applies to any device. Note, to convert kilowatt hour( kWh): 1 kWh = (1000 W) (3600 s) = 3.60 * 10^6 J.
Ohms Law: Resistance and Resistors
To produce an electric current in a circuit, a difference in potential is required. One way to produce a potential difference along a wire is to connect tis ends to opposite terminals of a battery. Experimentally Ohm established that the current in a metal wire is proportional to the potential difference V applied to its two ends. If for example we connect a wire to the terminals ofa. 6 V battery, the current in the wire will be twice what it would be if the wire were connected to a 3-V battery. ITs also found that reversing the sign of the voltage doesn't affect the magnitude of the current.
Peak Current Equations
Using equation V = IR, also applies to ac: if a voltage V exists across a resistance R, then the current I through the resistance is: I = V/R = V0/R * sinω*t = I0 * sinω*t The quantity I0 = V0/R is the peak current.
Voltas Key Research and discovery of the voltaic battery
Voltas research found that certain combinations of metals produced a greater effect than others, and, using his measurements, listed them in order of effectiveness. He also found carbon could be used in place of one of the metals. Thus he conceived his greatest contribution, a voltaic battery where there was a disc of zinc and one of silver, he placed a piece of cloth or paper soaked in salt solution or dilute acid and piled a 'battery' of such couplings, one on top of another. This pile or battery produced a much increased potential difference. Indeed, when strips of metal connected to the two ends of the piles were brought close, a spark was produced. Thus he built and designed the first electric battery.
Direct vs Alternating Current
When a battery is connected to a circuit, the current moves steadily in one direction. This is called a direct current, or dc. Electric generators at electric power plants, however, produce alternating current, or ac. An alternating current reverse direction many times per second and is commonly sinusoidal. The electrons in a wire first move in one direction and then in the other. The current supplied to homes and businesses by electric companies is ac throughout almost the entire world.
Conventional Current
When the conventions of positive and negative charge it was assumed the positive charge flowed in a wire. For nearly all purposes, positive charge flowing in one direction is exactly equivalent to negative charge flowing in the opposite direction. When we speak of the current direction in a circuit, we mean the direction positive charge wouuld flow. This is referred to as conventional current. When we want to speak of the direction of electron flow, we specifically state its electron current. In liquids and gases both positive and negative charge ions can move. Note: Another unit you can see is ampere-hour (A *h) from Delta Q = I * Delta t
