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5: Electric Current 5.1 Electric potential difference, current and resistance

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Electric Circuits The instant a circuit is turned on, an electrical field develops (moving through the circuit at about the speed of light). The field acts upon charged bodies. Thus the free electrons in a wire (or other charge carriers e.g. ions in liquids) begin to move almost simultaneously and reach speeds up to 1/1000 x speed of light. Constant interactions (collisions) with atoms reduce the average speed of electrons in a wire to around 0.5mms -1. Q. Describe, in as much scientific detail as possible, what happens in an electric circuit when it is switched on.

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Energy and Work in Circuits In any electrical circuit energy is transferred from the power source (e.g. a cell or dynamo) to somewhere else (e.g. to internal energy in a heating element). Q. In a simple torch circuit, describe the energy changes occurring and describe what is doing the work and what is having work done upon it. Work is done by the cell on the electrons: the electric field exerts a force upon them that makes them move through a distance. The electrons interact with and do work upon the atoms in the lamp filament, causing them to vibrate more. Chemical energy Kinetic energy Internal energy (in cells) (of electrons)(of filament)

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Voltage Voltage can be thought of as a sort of electrical push. Voltage at a point is also called potential and can be measured at any point relative to another point. Thus the voltage across a component is better described as the potential difference. EMF V1V1 V2V2 V3V3 V4V4 - + V1V1 V2V2 V3V3 V4V4 electrons

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Potential Voltage at a point is called the point potential. Point potential is always measured relative to other points. E.g. the negative terminal of a cell or Earth can be taken as zero. Potential difference can then be determined from individual point potentials.

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E.g. If the potential at point A is 3.2V and point B is 1.2V what are the potential differences across R, M and L? Sketch the potential - position graph: 4.5V R M A B L + A B - potential (V)

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Potential Difference This can be defined as follows: The potential difference between any two points in an electrical circuit is equal to the work done moving one coulomb of charge from one point to the other. Potential difference = Work Charge V = W Q V = potential difference between two points in the circuit (Volts) W = work done (Joules) Q = charge (Coulombs)

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Electrical potential energy - + So as an electron moves between two points in a circuit, its potential energy will decrease and its kinetic energy will increase (ignoring collisions with atoms) by an amount equal to the work done by the electric field. So… W = QV KE = PE = qV E = change in energy(Joules) V = potential difference (Volts) q = charge of particle (Coulombs) Q. Calculate the potential energy lost by an electron as it moves from the negative to positive terminal of a 9 Volt cell. What happens to this energy? (e = - 1.6 x 10 -19 C)

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The Electronvolt When we are considering individual charged particles gaining or losing energy, a typical order of magnitude is 10 -18 Joules. Clearly the Joule is a cumbersome unit to use in this context. Instead we use another unit of energy - the electronvolt. One electronvolt (1eV) is the work done moving one electron through a potential difference of one volt. So… W = QV 1eV= (-1.6 x 10 -19 ) x -1 1eV= 1.6 x 10 -19 J

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Electric current Demo: The shuttling ball This demonstration shows that… One coulomb passes a point in a circuit when a current of one amp flows for one second. So… Q. From the shuttling ball demo, determine the… Number of coulombs flowing per second Number of electrons flowing per second Charge on the ball …electric current is the rate of flow of charge. ΔQ = I Δt ΔQ = Charge (Coulombs) I = Current (Amps) Δt = Time taken (seconds)

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Amp-hours A larger unit of charge, used in industrial and engineering applications is the Amp-hour (Ah). E.g. A 1.6 Ah cell can supply a current of 1.6A for one hour. Q1. Determine the charge stored in… a. A 2.4 Ah camcorder battery b. A 700 mAh mobile phone battery c. A 60 Ah battery for a lorry 8640 C 2520 C 2.16 x 10 5 C

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Q2. Find the total charge delivered by a car battery when current varies with use as shown.

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Defining the Ampere Demo: Force between two parallel wires One ampere is defined as the current which will produce an attractive force of 2×10 –7 Newton per metre of length between two straight, parallel conductors (of infinite length and negligible circular cross section) placed one metre apart.

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Resistance Resistance can be thought of as the opposition to flow of charge in a conductor. Thus… Resistance can be defined as the ratio of the potential difference across the conductor to the current flowing through it. R = V I R = Resistance (Ohms) V = P.d. (Volts) I = Current (Amps)

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Factors affecting resistance Experiment: Investigate the effect of length and cross sectional area of a wire upon its resistance. Results A V Use a similar circuit to this or an Ohmmeter to determine the relationships between… a. Length and R b. Cross sectional area and resistance. R length R area R 1 / area

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Resistivity The resistance of a wire is proportional to its length and inversely proportional to its cross sectional area. The resistance also depends upon the material which has a certain resistivity (ρ). Resistance = resistivity x length cross sectional area R = ρl A R = Resistance (Ω) l = Length of conductor (m) A = cross sectional area (m 2 ) ρ = resistivity (Ωm) Can you determine a unit for resistivity?

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E.g. The live rail of an electric railway has a c.s. area of 50cm 2. The resistivity of steel is 1.0 x 10 -7 Ωm. Ignoring the resistive effects of joints, determine the resistance per km.

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Strain Gauges Engineers use strain gauges to measure strain magnitude and distribution in structures, aircraft, bridges etc. (High strain regions can lead to failure). It is designed as a long wire folding back upon itself and is stuck onto surfaces. Q. What will happen to the resistance when the surface bends. Why?

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Ohms Law If an electrical conductor obeys Ohms law then… An Ohmic conductor has a constant ratio between the voltage and current. i.e. its resistance is constant. E.g. A carbon resistor is an Ohmic conductor. … the current flowing through the conductor is directly proportional to the potential difference across the conductor (so long as temperature is constant). V I

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Electrical Power Experiment: To determine the power of a lamp. A V 1.Measure I and V 2.Determine the charge that passes through the lamp in one minute 3.Determine the work done by the cell on the charge and lamp in one minute. 4.Now determine the work done in one second. What have you calculated?

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We know… so… W = QV but…Q = It and P = so… P = Note: For a resistor, substituting V = IR into P = IV gives… V = W Q W t ItV t P = IV Power dissipated = I 2 R or P = V 2 R

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