CURRENT ELECTRICITY

Electricity is the most versatile energy source that we have; it is also one of the newest: homes and businesses have been using it for not much more than a hundred years. Electricity has played a vital part of our past. But it could play a different role in our future, with many more buildings generating their own renewable electric power using solar cells and wind turbines. Let's take a closer look at electricity and find out how it works!

Electricity is a type of energy that can build up in one place or flow from one place to another. When electricity gathers in one place it is known as static electricity (the word static means something that does not move); electricity that moves from one place to another is called current electricity.

Current electricityWhen electrons move, they carry electrical energy from one place to another. This is called current electricity or an electric current. . Electric currents are involved in powering all the electrical appliances that you use, from washing machines to flashlights and from telephones to MP3 players.

.Have you heard of the terms potential energy and kinetic energy? Potential energy means energy that is stored somehow for use in the future. A car at the top of a hill has potential energy, because it has the potential (or ability) to roll down the hill in future. When it's rolling down the hill, its potential energy is gradually converted into kinetic energy (the energy something has because it's moving).

Static electricity and current electricity are like potential energy and kinetic energy. When electricity gathers in one place, it has the potential to do something in the future. Electricity stored in a battery is an example of electrical potential energy. You can use the energy in the battery to power a flashlight, for example. When you switch on a flashlight, the battery inside begins to supply electrical energy to the lamp, making it give off light. All the time the light is switched on, energy is

CURRENT ELECTRICITYflowing from the battery to the lamp. Over time, the energy stored in the battery is gradually turned into light (and heat) in the lamp.

Electric circuitsFor an electric current to happen, there must be a circuit. A circuit is a closed path or loop around which an electric current flows. A circuit is usually made by linking electrical components together with pieces of wire cable. Thus, in a flashlight, there is a simple circuit with a switch, a lamp, and a battery linked together by a few short pieces of copper wire. When you turn the switch on, electricity flows around the circuit. If there is a break anywhere in the circuit, electricity cannot flow. If one of the wires is broken, for example, the lamp will not light. Similarly, if the switch is turned off, no electricity can flow.

Materials such as copper metal that conduct electricity (allow it to flow freely) are called conductors. Materials that don't allow electricity to pass through them so readily, such as rubber and plastic, are called insulators. What makes copper a conductor and rubber an insulator?A current of electricity is a steady flow of electrons. When electrons move from one place to another, round a circuit, they carry electrical energy from place to place like marching ants carrying leaves. Instead of carrying leaves, electrons carry a tiny amount of electric chargeElectricity can travel through something when its structure allows electrons to move through it easily. Metals like copper have "free" electrons that are not bound tightly to their parent atoms. These electrons flow freely throughout the structure of copper and this is what enables an electric current to flow. In rubber, the electrons are more tightly bound. There are no "free" electrons and, as a result, electricity does not really flow through rubber at all.

CURRENT ELECTRICITYConductors that let electricity flow freely are said to have a high conductance and a low resistance; insulators that do not allow electricity to flow are the opposite: they have a low conductance and a high resistance.We can't always generate electricity where and when it is needed so batteries, devices that store electrical energy in chemical form, are very important. .

All batteries contain one or more cells, but people often use the terms battery and cell interchangeably. A cell is just the working chemical unit inside a battery; one battery can contain any number of cells. A cell has three main parts: a positive electrode (terminal), a negative electrode, and a liquid or solid separating them called the electrolyte. When a battery is connected to an electric circuit, a chemical reaction takes place in the electrolyte causing ions (in this case, atoms with a positive electrical charge) to flow through it one way, with electrons (particles with a negative charge) flowing through the outer circuit in the other direction. This movement of electric charge

makes an electric current flow through the cell and through the circuit it is connected to. It's important to note that the electrodes in a battery are always made from two dissimilar materials (so never both from the same metal, for example). This is the key to how and why a battery works: one of the materials "likes" to give up electrons, the other likes to receive them. If both electrodes were made from the same material, that wouldn't happen and no current would flow.

Measuring electricity We can measure electricity in a number of different ways, but a few measurements are particularly important.

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-Electrical resistance The electrical resistance of an electrical conductor is a measure of the difficulty to pass an electric current through that conductor.

Suppose you're trying to force water through a pipe. Different sorts of pipes will be more or less obliging, so a fatter pipe will resist the water less than a thinner one and a shorter pipe will offer less resistance than a longer one. If you fill the pipe with, say, pebbles or sponge, water will still trickle through it but much more slowly. In other words, the length, cross-sectional area (the area you see looking into the pipe to see what's inside), and stuff inside the pipe all affect its resistance to water.

Electrical resistors are very similar—affected by the same three factors. If you make a wire thinner or longer, it's harder for electrons to wiggle through it. And, as we've already seen, it's harder for electricity to flow through some materials (insulators) than others (conductors). Although Georg Ohm is best known for relating voltage, current, and resistance, he also researched the relationship between resistance and the size and type of material from which a resistor is made. That led him to another important equation:

R = ρ × L / A

In simple words, the resistance (R) of a material increases as its length increases (so longer wires offer more resistance) and increases as its area decreases (thinner wires offer more resistance). The resistance is also related to the type of material from which a resistor is made, and that's indicated in this equation by the symbol ρ, which is called the resistivity, and measured in units of Ωm (ohm meters). Different materials have very different resistivities: conductors have much lower resistivity than insulators. At room temperature, aluminum comes in at about 2.8 x 10−8 Ωm, while copper (a better conductor) is significantly lower at 1.7 −8 Ωm. Silicon (a semiconductor) has a resistivity of about 1000 Ωm and glass (a good insulator) measures about

CURRENT ELECTRICITY1012 Ωm. You can see from these figures how vastly different conductors and insulators are in their ability to carry electricity: silicon is about 100 billion times worse than copper and glass is about a billion times worse again!

R is the resistance in ohms (Ω).ρ is the resistivity in ohms-meter (Ω×m)l is the length of the conductor in meter (m)A is the cross sectional area of the conductor in square meters (m2) -Voltage The voltage is a kind of electrical force that makes electricity move through a wire and we measure it in volts. The bigger the voltage, the more current will tend to flow. So a 12-volt car battery will generally produce more current than a 1.5-volt flashlight battery.

-CurrentVoltage does not, itself, go anywhere: it's quite wrong to talk about voltage "flowing through" things. What moves through the wire in a circuit is electrical current: a steady flow of electrons, measured in amperes (or amps).

I = Q ÷ t

I is the current in amperes (amps), AQ is the charge in coulombs, Ct is the time in seconds, s

CURRENT ELECTRICITY

Ohm´s lawWhen you first learn about electricity, you discover that materials fall into two basic categories called conductors and insulators. Conductors (such as metals) let electricity flow through them; insulators (such as plastics and wood) generally do not. But nothing's quite so simple, is it? Any substance will conduct electricity if you put a big enough voltage across it: even air, which is normally an insulator, suddenly becomes a conductor when a powerful voltage builds up in the clouds—and that's what makes lightning. Rather than talking about conductors and insulators, it's often clearer to talk about resistance: the ease with which something will let electricity flow through it. A conductor has low resistance, while an insulator has much higher resistance. Electricity flows through a material carried by electrons, tiny charged particles inside atoms. Broadly speaking, materials that conduct electricity well are ones that allow electrons to flow freely through them. In metals, for example, the atoms are locked into a solid, crystalline structure (a bit like a metal climbing frame in a playground). Although most of the electrons inside these atoms are fixed in place, some can swarm through the structure carrying electricity with them. That's why metals are good conductors: a metal puts up relatively little resistance to electrons flowing through it. Plastics are entirely different. Although often solid, they don't have the same crystalline structure. Their molecules (which are typically very long, repetitive chains called polymers) are bonded together in such a way that the electrons inside the atoms are fully occupied. There are, in short, no free electrons that can move about in plastics to carry an electric current. Plastics are good insulators: they put up a high resistance to electrons flowing through them.

This is all a little vague for a subject like electronics, which requires precise control of electric currents. That's why we define resistance more precisely as the voltage in volts required to make a current of 1 amp flow through a circuit. If it takes 500 volts to make 1 amp flow, the resistance is 500 ohms (written 500 Ω). You might see this relationship written out as a mathematical equation:

CURRENT ELECTRICITY

V = I × R

This is known as Ohm's Law for German physicist Georg Simon Ohm (1789–1854).

Circuit diagrams

When there are two or more electrical devices present in a circuit with an energy source, there are a couple of basic means by which to connect them. They can be connected in series or connected in parallel. Suppose that there are three light bulbs connected together in the same circuit. If connected in series, then they are connected in such a way that an individual charge would pass through each one of the light bulbs in consecutive fashion. When in series, charge passes through every light bulb. If connected in parallel, a single charge passing through the external circuit would only pass through one of the light bulbs. The light bulbs are placed within a separate branch line, and a charge traversing the external circuit will pass through only one of the branches during its path back to the low potential terminal. The means by which the resistors are connected will have a major effect upon the overall resistance of the circuit, the total current in the circuit, and the current in each resistor.

The main questions of concern in are typically the following:

CURRENT ELECTRICITYAs the number of resistors (light bulbs) increases, what happens to the overall current within the circuit?As the number of resistors (light bulbs) increases, what happens to the overall resistance within the circuit?If one of the resistors is turned off (i.e., a light bulb goes out), what happens to the other resistors (light bulbs) in the circuit? Do they remain on (i.e., lit)?

-Exploring Series Connections

A series circuit can be constructed by connecting light bulbs in such a manner that there is a single pathway for charge flow; the bulbs are added to the same line with no branching point. As more and more light bulbs are added, the brightness of each bulb gradually decreases. This observation

is an indicator that the current within the circuit is decreasing.So for series circuits, as more resistors are added the overall current within the circuit decreases. This decrease in current is consistent with the conclusion that the overall resistance increases.

A final observation that is unique to series circuits is the effect of removing a bulb from a socket. If one of three bulbs in a series circuit is unscrewed from its socket, then it is observed that the other bulbs immediately go out. In order for the devices in a series circuit to work, each device must work. If one goes out, they all go out. Suppose that all the appliances in a household kitchen were all connected in series. In order for the refrigerator to work in that kitchen, the toaster oven, dishwasher, garbage disposal and overhead light would all have to be on. In order for one device in series to work, they all must work. If current is cut from any one of them, it is cut from all of them. Quite obviously, the appliances in the kitchen are not connected in series.

-Exploring Parallel Connections

Using the same collection of wires, D-cells and bulbs, parallel circuits can be explored in the same manner. The effect of the number of resistors upon the overall current and the overall resistance can be investigated. The diagrams below depict the usual means of constructing the circuit with

CURRENT ELECTRICITYparallel connections of light bulbs. One will note that a study of the overall current for parallel connections requires the addition of an indicator bulb. The indicator bulb is placed outside of the branches and allows one to observe the effect of additional resistors upon the overall current. The bulbs that are placed in the parallel branches only provide an indicator of the current through that particular branch. So if investigating the effect of the number of resistors upon the overall current and resistance, one must make careful observations of the indicator bulb, not the bulbs that are placed in the branches. The diagram below depicts the typical observations.

It is clear from observing the indicator bulbs in the above diagrams that the addition of more resistors causes the indicator bulb to get brighter. For parallel circuits, as the number of resistors increases, the overall current also increases. This increase in current is consistent with a decrease in overall resistance. Adding more resistors in a separate branch has the unexpected result of decreasing the overall resistance!

If an individual bulb in a parallel branch is unscrewed from its socket, then there is still current in the overall circuit and current in the other branches. Removing the third bulb from its socket has the effect of transforming the circuit from a three-bulb parallel circuit to a two-bulb parallel circuit. If the appliances in a household kitchen were connected in parallel, then the refrigerator could function without having to have the dishwasher, toaster, garbage disposal and overhead lights on. One appliance can work without the other appliances having to be on. Since each appliance is in its own separate branch, turning that appliance off merely cuts off the flow of charge to that branch. There will still be charge flowing through the other branches to the other appliances. Quite obviously, the appliances in a home are wired with parallel connections.The effect of adding resistors is quite different if added in parallel compared to adding them in series. Adding more resistors in series means that there is more overall resistance; yet adding more resistors in parallel means that there is less overall resistance. The fact that one can add

CURRENT ELECTRICITYmore resistors in parallel and produce less resistance is quite bothersome to many. An analogy may help to clarify the reason behind this initially bothersome truth.

The flow of charge through the wires of a circuit can be compared to the flow of cars along a tollway system in a very crowded metropolitan area. The main sources of resistance on a tollway system are the tollbooths. Stopping cars and forcing them to pay a toll at a tollbooth not only slows the cars down, but in a highly trafficked area, will also cause a bottleneck with a backup for miles. The rate at which cars flow past a point on that tollway system is reduced significantly by the presence of a tollbooth. Clearly, tollbooths are the main resistor to car flow.

Now suppose that in an effort to increase the flow rate the Tollway Authority decides to add two more tollbooths at a particular toll station where the bottleneck is troublesome to travelers. They consider two possible means of connecting their tollbooths - in series versus in parallel. If adding the tollbooths (i.e., resistors) in series, they would add them in a manner that every car flowing along the highway would have to stop at each tollbooth in consecutive fashion. With only one pathway through the tollbooths, each car would have to stop and pay a toll at each booth. Instead of paying 60 cents one time at one booth, they would now have to pay 20 cents three times at each of the three tollbooths. Quite obviously, adding tollbooths in series would have the overall effect of increasing the total amount of resistance and decreasing the overall car flow rate (i.e., current).

The other means of adding the two additional tollbooths at this particular toll station would be to add the tollbooths in parallel fashion. Each tollbooth could be placed in a separate branch. Cars flowing along the tollway would stop at only one of the three booths. There would be three possible pathways for cars to flow through the toll station and each car would chose only one of the pathways. Quite obviously, adding tollbooths in parallel would have the overall effect of decreasing the total amount of resistance and increasing the overall car flow rate (i.e.,

current) along the tollway. Just as is the case for adding more electrical resistors in parallel, adding more tollbooths in parallel branches creates less overall resistance. By allowing for more pathways (i.e., branches) by which charge and cars can flow through the bottleneck areas, the flow rate can be increased.

CURRENT ELECTRICITY

When analyzing combination circuits, it is critically important to have a solid understanding of the concepts that pertain to both series circuits and parallel circuits. Since both types of connections are used in combination circuits, the concepts associated with both types of circuits apply to the respective parts of the circuit. The main concepts associated with series and parallel circuits are organized in the table below.

-Series Circuits

The current is the same in every resistor; this current is equal to that in the battery.The sum of the voltage drops across the individual resistors is equal to the voltage rating of the battery.The overall resistance of the collection of resistors is equal to the sum of the individual resistance values,

Rtot = R1 + R2 + R3 + ...

-Parallel Circuits

The voltage drop is the same across each parallel branch.The sum of the current in each individual branch is equal to the current outside the branches.The equivalent or overall resistance of the collection of resistors is given by the equation

1/Req = 1/R1 + 1/R2 + 1/R3 ...

Each of the above concepts has a mathematical expression. Combining the mathematical expressions of the above concepts with the Ohm's law equation (ΔV = I • R) allows one to conduct a complete analysis of a combination circuit.

Analysis of Combination Circuits

The basic strategy for the analysis of combination circuits involves using the meaning of equivalent resistance for parallel branches to transform the combination circuit into a series circuit. Once transformed into a series circuit, the analysis can be conducted in the usual manner.

CURRENT ELECTRICITY

By applying one's understanding of the equivalent resistance of parallel branches to a combination circuit, the combination circuit can be transformed into a series circuit. Then an understanding of the equivalent resistance of a series circuit can be used to determine the total resistance of the circuit. Consider the following diagrams below. Diagram A represents a combination circuit with resistors R2 and R3 placed in parallel branches. Two 4-Ω resistors in parallel is equivalent to a resistance of 2 Ω. Thus, the two branches can be replaced by a single resistor with a resistance of 2 Ω. This is shown in Diagram B. Now that all resistors are in series, the formula for the total resistance of series resistors can be used to determine the total resistance of this circuit

Example 1:The first example is the easiest case - the resistors placed in parallel have the same resistance. The goal of the analysis is to determine the current in and the voltage drop across each resistor.

As discussed above, the first step is to simplify the circuit by replacing the two parallel resistors with a single resistor that has an equivalent resistance. Two 8 Ω resistors in series is equivalent to a single 4 Ω resistor. Thus, the two branch resistors (R2 and R3) can be replaced by a single resistor with a resistance of 4 Ω. This 4 Ω resistor is in series with R1 and R4. Thus, the total resistance is

CURRENT ELECTRICITY

Rtot = R1 + 4 Ω + R4 = 5 Ω + 4 Ω + 6 ΩRtot = 15 Ω

Now the Ohm's law equation (ΔV = I • R) can be used to determine the total current in the circuit. In doing so, the total resistance and the total voltage (or battery voltage) will have to be used.

Itot = ΔVtot / Rtot = (60 V) / (15 Ω)Itot = 4 Amp

The 4 Amp current calculation represents the current at the battery location. Yet, resistors R1 and R4 are in series and the current in series-connected resistors is everywhere the same. Thus,

Itot = I1 = I4 = 4 AmpFor parallel branches, the sum of the current in each individual branch is equal to the current outside the branches. Thus, I2 + I3 must equal 4 Amp. There are an infinite number of possible values of I2 and I3 that satisfy this equation. Since the resistance values are equal, the current values in these two resistors are also equal. Therefore, the current in resistors 2 and 3 are both equal to 2 Amp.

I2 = I3 = 2 AmpNow that the current at each individual resistor location is known, the Ohm's law equation (ΔV = I • R) can be used to determine the voltage drop across each resistor. These calculations are shown below.

ΔV1 = I1 • R1 = (4 Amp) • (5 Ω)ΔV1 = 20 VΔV2 = I2 • R2 = (2 Amp) • (8 Ω)

ΔV2 = 16 VΔV3 = I3 • R3 = (2 Amp) • (8 Ω)

ΔV3 = 16 VΔV4 = I4 • R4 = (4 Amp) • (6 Ω)

ΔV4 = 24 V

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The analysis is now complete and the results are summarized in the diagram below.

Example 2:The second example is the more difficult case - the resistors placed in parallel have a different resistance value. The goal of the analysis is the same - to determine the current in and the voltage drop across each resistor

As

discussed above, the first step is to simplify the circuit by replacing the two parallel resistors with a single resistor with an equivalent resistance. The equivalent resistance of a 4-Ω and 12-Ω resistor placed in parallel can be determined using the usual formula for equivalent resistance of parallel branches:

1 / Req = 1 / R1 + 1 / R2 + 1 / R3 ...1 / Req = 1 / (4 Ω) + 1 / (12 Ω)

1 / Req = 0.333 Ω-1

CURRENT ELECTRICITYReq = 1 / (0.333 Ω-1)

Req = 3.00 Ω

Based on this calculation, it can be said that the two branch resistors (R2 and R3) can be replaced by a single resistor with a resistance of 3 Ω. This 3 Ω resistor is in series with R1 and R4. Thus, the total resistance is

Rtot = R1 + 3 Ω + R4 = 5 Ω + 3 Ω + 8 ΩRtot = 16 Ω

Now the Ohm's law equation (ΔV = I • R) can be used to determine the total current in the circuit. In doing so, the total resistance and the total voltage (or battery voltage) will have to be used.

Itot = ΔVtot / Rtot = (24 V) / (16 Ω)Itot = 1.5 Amp

The 1.5 Amp current calculation represents the current at the battery location. Yet, resistors R1 and R4 are in series and the current in series-connected resistors is everywhere the same. Thus,

Itot = I1 = I4 = 1.5 AmpFor parallel branches, the sum of the current in each individual branch is equal to the current outside the branches. Thus, I2 + I3 must equal 1.5 Amp. There are an infinite possibilities of I2 and I3 values that satisfy this equation. In the previous example, the two resistors in parallel had the identical resistance; thus the current was distributed equally among the two branches. In this example, the unequal current in the two resistors complicates the analysis. The branch with the least resistance will have the greatest current. Determining the amount of current will demand that we use the Ohm's law equation. But to use it, the voltage drop across the branches must first be known. So the direction that the solution takes in this example will be slightly different than that of the simpler case illustrated in the previous example.

To determine the voltage drop across the parallel branches, the voltage drop across the two series-connected resistors (R1 and R4) must first be determined. The Ohm's law equation (ΔV = I • R) can be used to determine the voltage drop across each resistor. These calculations are shown below.

ΔV1 = I1 • R1 = (1.5 Amp) • (5 Ω)

CURRENT ELECTRICITYΔV1 = 7.5 VΔV4 = I4 • R4 = (1.5 Amp) • (8 Ω)

ΔV4 = 12 VThis circuit is powered by a 24-volt source. Thus, the cumulative voltage drop of a charge traversing a loop about the circuit is 24 volts. There will be a 19.5 V drop (7.5 V + 12 V) resulting from passage through the two series-connected resistors (R1 and R4). The voltage drop across the branches must be 4.5 volts to make up the difference between the 24 volt total and the 19.5-volt drop across R1 and R4. Thus,

ΔV2 = V3 = 4.5 VKnowing the voltage drop across the parallel-connected resistors (R1 and R4) allows one to use the Ohm's law equation (ΔV = I • R) to determine the current in the two branches.

I2 = ΔV2 / R2 = (4.5 V) / (4 Ω)I2 = 1.125 AI3 = ΔV3 / R3 = (4.5 V) / (12 Ω)

I3 = 0.375 AThe analysis is now complete and the results are summarized in the diagram below.

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Electric PowerThe electric power P is equal to the energy consumption E divided by the consumption time t:

P is the electric power in watt (W).E is the energy consumption in joule (J).t is the time in seconds (s).

-ExampleFind the electric power of an electrical circuit that consumes 120 joules for 20 seconds.Solution:E = 120Jt = 20sP = E / t = 120J / 20s = 6W

Together, voltage and current give you electrical power. The bigger the voltage and the bigger the current, the more electrical power you have. We measure electric power in units called watts. Something that uses 1 watt uses 1 joule of energy each second.

P= V x I

The electric power in a circuit is equal to the voltage × the current (in other words: watts = volts × amps). So if you have a 100-watt (100 W) light and you know your electricity supply is rated as 220 volts (typical household voltage ithe United States ), the current flowing must be 100/120 = 0.8 amps. If you're in Europe, your household voltage is more likely 230 volts. So if you use the same 100-watt light, the current flowing is 100/230 = 0.4 amps. The light burns just as brightly in both countries and uses the same amount of power in each case; in Europe it uses a higher voltage and lower current; in the States, there's a lower voltage and higher current. (One quick note: 120 volts and 230 volts are the "nominal" or standard household voltages—the voltages you're supposed to have, in theory. In practice, your home might have more or less voltage than this, for all sorts of reasons, but mainly because of how far you are from your local power plant or power supply.)

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Energy

Power is a measurement of how much energy you're using each second. To find out the total amount of energy an electric appliance uses, you have to multiply the power it uses per second by the total number of seconds you use it for. The result you get is measured in units of power × time,

E = P x t (J)

, often converted into a standard unit called the kilowatt hour (kWh).1kWh = 3.6x10+6 J

If you used an electric toaster rated at 1000 watts (1 kilowatt) for a whole hour, you'd use 1 kilowatt hour of energy; you'd use the same amount of energy burning a 2000 watt toaster for 0.5 hours or a 100-watt lamp for 10 hours