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Electric Currents Topic 5 .1 Electric potential difference, current and resistance
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Electric Potential Energy <ul><li>If you want to move a charge closer to a charged sphere you have to push against the repulsive force </li></ul><ul><li>You do work and the charge gains electric potential energy. </li></ul><ul><li>If you let go of the charge it will move away from the sphere, losing electric potential energy, but gaining kinetic energy. </li></ul>
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<ul><li>When you move a charge in an electric field its potential energy changes. </li></ul><ul><li>This is like moving a mass in a gravitational field. </li></ul>
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<ul><li>The electric potential V at any point in an electric field is the potential energy that each coulomb of positive charge would have if placed at that point in the field. </li></ul><ul><li>The unit for electric potential is the joule per coulomb (J C ‑1 ), or the volt (V). </li></ul><ul><li>Like gravitational potential it is a scalar quantity. </li></ul>
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<ul><li>In the next figure, a charge +q moves between points A and B through a distance x in a uniform electric field. </li></ul><ul><li>The positive plate has a high potential and the negative plate a low potential. </li></ul><ul><li>Positive charges of their own accord, move from a place of high electric potential to a place of low electric potential. </li></ul><ul><li>Electrons move the other way, from low potential to high potential. </li></ul>
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<ul><li>In moving from point A to point B in the diagram, the positive charge +q is moving from a low electric potential to a high electric potential. </li></ul><ul><li>The electric potential is therefore different at both points. </li></ul>
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<ul><li>In order to move a charge from point A to point B, a force must be applied to the charge equal to qE </li></ul><ul><li>(F = qE). </li></ul><ul><li>Since the force is applied through a distance x, then work has to be done to move the charge, and there is an electric potential difference between the two points. </li></ul><ul><li>Remember that the work done is equivalent to the energy gained or lost in moving the charge through the electric field. </li></ul>
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Electric Potential Difference <ul><li>Potential difference </li></ul><ul><li>We often need to know the difference in potential between two points in an electric field </li></ul><ul><li>The potential difference or p.d. is the energy transferred when one coulomb of charge passes from one point to the other point. </li></ul>
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<ul><li>The diagram shows some values of the electric potential at points in the electric field of a positively‑charged sphere </li></ul><ul><li>What is the p.d. between points A and B in the diagram? </li></ul>
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<ul><li>When one coulomb moves from A to B it gains 15 J of energy. </li></ul><ul><li>If 2 C move from A to B then 30 J of energy are transferred. In fact: </li></ul>
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Change in Energy <ul><li>Energy transferred, </li></ul><ul><li>This could be equal to the amount of electric potential energy gained or to the amount of kinetic energy gained </li></ul><ul><li>W =charge, q x p.d.., V </li></ul><ul><li>(joules) (coulombs) (volts) </li></ul>
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The Electronvolt <ul><li>One electron volt (1 eV) is defined as the energy acquired by an electron as a result of moving through a potential difference of one volt. </li></ul><ul><li>Since W = q x V </li></ul><ul><li>And the charge on an electron or proton is 1.6 x 10 -19 C </li></ul><ul><li>Then W = 1.6 x 10 -19 C x 1V </li></ul><ul><li>W = 1.6 x 10 -19 J </li></ul><ul><li>Therefore 1 eV = 1.6 x 10 -19 J </li></ul>
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Conduction in Metals <ul><li>A copper wire consists of millions of copper atoms. </li></ul><ul><li>Most of the electrons are held tightly to their atoms, but each copper atom has one or two electrons which are loosely held. </li></ul><ul><li>Since the electrons are negatively charged, an atom that loses an electron is left with a positive charge and is called an ion. </li></ul>
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<ul><li>The diagram shows that the copper wire is made up of a lattice of positive ions, surrounded by free' electrons: </li></ul><ul><li>The ions can only vibrate about their fixed positions, but the electrons are free to move randomly from one ion to another through the lattice. </li></ul><ul><li>All metals have a structure like this. </li></ul>
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What happens when a battery is attached to the copper wire? <ul><li>The free electrons are repelled by the negative terminal and attracted to the positive one. </li></ul><ul><li>They still have a random movement, but in addition they all now move slowly in the same direction through the wire with a steady drift velocity. </li></ul><ul><li>We now have a flow of charge ‑ we have electric current. </li></ul>
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Electric Current <ul><li>Current is measured in amperes (A) using an ammeter. </li></ul><ul><li>The ampere is a fundamental unit. </li></ul><ul><li>The ammeter is placed in the circuit so that the electrons pass through it. </li></ul><ul><li>Therefore it is placed in series. </li></ul><ul><li>The more electrons that pass through the ammeter in one second, the higher the current reading in amps. </li></ul>
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<ul><li>1 amp is a flow of about 6 x 10 18 electrons in each second! </li></ul><ul><li>The electron is too small to be used as the basic unit of charge, so instead we use a much bigger unit called the coulomb (C). </li></ul><ul><li>The charge on 1 electron is </li></ul><ul><li>only 1.6 x 10 ‑19 C. </li></ul>
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<ul><li>In fact: </li></ul>Or I = Δ q/ Δ t Current is the rate of flow of charge
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<ul><li>Which way do the electrons move? </li></ul><ul><ul><li>At first, scientists thought that a current was made up of positive charges moving from positive to negative. </li></ul></ul><ul><ul><li>We now know that electrons really flow the opposite way, but unfortunately the convention has stuck. </li></ul></ul><ul><ul><li>Diagrams usually show the direction of `conventional current' going from positive to negative, but you must remember that the electrons are really flowing the opposite way. </li></ul></ul>
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Resistance <ul><li>A tungsten filament lamp has a high resistance, but connecting wires have a low resistance. </li></ul><ul><li>What does this mean? </li></ul><ul><li>The greater the resistance of a component, the more difficult it is for charge to flow through it. </li></ul>
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<ul><li>The electrons make many collisions with the tungsten ions as they move through the filament. </li></ul><ul><li>But the electrons move more easily through the copper connecting wires because they make fewer collisions with the copper ions. </li></ul>
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<ul><li>Resistance is measured in ohms ( Ω ) and is defined in the following way: </li></ul><ul><ul><li>The resistance of a conductor is the ratio of the p.d. applied across it, to the current passing through it. </li></ul></ul><ul><li>In fact: </li></ul>
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Resistors <ul><li>Resistors are components that are made to have a certain resistance. </li></ul><ul><li>They can be made of a length of nichrome wire. </li></ul>
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Ohm’s Law <ul><li>The current through a metal wire is directly proportional to the p.d. across it (providing the temperature remains constant). </li></ul><ul><li>This is Ohm's law. </li></ul><ul><li>Materials that obey Ohm's law are called ohmic conductors. </li></ul>
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<ul><li>When X is a metal resistance wire the graph is a straight line passing through the origin: (if the temperature is constant) </li></ul><ul><li>This shows that: I is directly proportional to V. </li></ul><ul><li>If you double the voltage, the current is doubled and so the value of V/ I is always the same. </li></ul><ul><li>Since resistance R =V/I, the wire has a constant resistance. </li></ul><ul><li>The gradient is the resistance on a V against I graph, and 1/resistance in a I against V graph. </li></ul>
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<ul><li>Doubling the voltage produces less than double the current. </li></ul><ul><li>This means that the value of V/I rises as the current increases. </li></ul><ul><li>As the current increases, the metal filament gets hotter and the resistance of the lamp rises. </li></ul>
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<ul><li>The graphs for the wire and the lamp are symmetrical. </li></ul><ul><li>The current‑voltage characteristic looks the same, regardless of the direction of the current. </li></ul>
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