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Electricity

Understand electric current, voltage, and resistance. Learn about charge carriers and measuring units like volts, amps, and ohms. Explore DC and AC currents, Kirchoff's laws, and calculate charge and current relationships in circuits.

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Electricity

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  1. Electricity W Richards The Weald School

  2. Electric Current Note that electrons go from negative to positive + - e- e- Electric current is a flow of negatively charged particles (i.e. electrons). We call them “charge carriers”

  3. Conventional Current + - As we said, technically electrons go from negative to positive. However, we usually talk about “conventional current” and we say that current moves from positive to negative:

  4. Basic ideas… Electric current is when electrons start to flow around a circuit. We use an _________ to measure it and it is measured in ____. Potential difference (also called _______) is how big the push on the electrons is. We use a ________ to measure it and it is measured in ______, a unit named after Volta. Resistance is anything that resists an electric current. It is measured in _____. Words: volts, amps, ohms, voltage, ammeter, voltmeter

  5. More basic ideas… If a battery is added the current will ________ because there is a greater _____ on the electrons so they move ______ If a bulb is added the current will _______ because there is greater ________ in the circuit, so the electrons move _____ Words – faster, decrease, slower, increase, push, resistance

  6. DC and AC V DC stands for “Direct Current” – the current only flows in one direction: Time 1/50th s AC stands for “Alternating Current” – the electrons change direction 50 times every second (frequency = 50Hz) 240V T V

  7. Charge and Current PROTON – positively charged ELECTRON – negatively charged Recall the structure of an atom: • Notice: • Atoms have the same number of protons and electrons – they are NEUTRAL overall • Because electrons are on the outside of the atoms they can move around (this is what causes electrical effects)

  8. Static Electricity + - - + Static electricity is when charge “builds up” on an object and then stays “static”. How the charge builds up depends on what materials are used: + + - - + + + - - - + + - + - -

  9. Static Electricity - - + - - + + - - - - -

  10. Measuring Charge • The charge on an electron is very small, so we measure charge using units called “coulombs” (C). • One electron has a charge of 1.6 x 10-19 C. • Charge can be measured using a coulombmeter, and they usually measure in nanocoloumbs (1nC = 10-9 C). • For example, a charged polythene rod may carry a charge of a few hundred nanocoulombs

  11. Calculating Charge (Q) Current = rate of flow of charge I =ΔQ ΔT By definition, current is the rate of flow of charge. In other words, its how much charge flows per second. One amp (1 A) is equal to one coulomb per second (1 Cs-1). Charge and current are related by the equation: • A battery supplies 10 C over a period of 50 seconds. What is the current? • Another battery is connected for 2 minutes and provided a current of 0.4 A. How much charge flowed? • A car battery has a capacity of 24 Ah (amp hours). If it provides a current of 48A how long can it be used for? How much charge (in coulombs) does it contain?

  12. Current in a series circuit If the current here is 2 amps… The current here will be… The current here will be… And the current here will be… In other words, the current in a series circuit is THE SAME at any point.

  13. Current in a parallel circuit Here comes the current… Half of the current will go down here (assuming the bulbs are the same)… And the rest will go down here… A PARALLEL circuit is one where the current has a “choice of routes”

  14. Current in a parallel circuit And the current here will be… The current here will be… The current here will be… The current here will be… If the current here is 6 amps

  15. Some example questions… 3A 6A

  16. Kirchoff’s First Law 6A Gustav Kirchoff (1824-1887) … then the current here will be 6A If the current through here is 4A... …and the current through here is 2A… “The sum of the currents leaving a point is the same as the sum of the currents entering that point.” For example:

  17. Voltage + - e- e- Earlier on we said that current is when electrons move: “Voltage” is the force that pushes the electrons. For electrons to move there must be a “voltage difference”, sometimes called a “potential difference” (p.d.). A higher p.d. means a stronger push, which causes an increase in current.

  18. Voltage in a series circuit V If the voltage across the battery is 6V… …and these bulbs are all identical… V V …what will the voltage across each bulb be? 2V

  19. Voltage in a series circuit V If the voltage across the battery is 6V… …what will the voltage across two bulbs be? V 4V

  20. Voltage in a parallel circuit If the voltage across the batteries is 4V… What is the voltage here? V V And here? 4V 4V

  21. Summary In a SERIES circuit: Current is THE SAME at any point Voltage SPLITS UP over each component In a PARALLEL circuit: Current SPLITS UP down each “strand” Voltage is THE SAME across each”strand”

  22. An example question: 6V A3 3A A1 V1 A2 V2 V3

  23. Another example question: 10V A3 3A A1 V1 A2 V2 V3

  24. Electromotive force and p.d. The sum of these EMFs… Is equal to the sum of the p.d.s Components like batteries and power supplies provide a force that pushes the current around a circuit: we call this the “electromotive force” (e.m.f). Other components like bulbs and motors have work done to them by the current – the voltage across them is called the “potential difference” (p.d.) Definition of EMF – “the total work done by a cell per coulomb of charge”

  25. Kirchoff’s Second Law Gustav Kirchoff (1824-1887) If the e.m.f of the batteries is 3V The voltage across each bulb will be 1V “Around any closed loop, the sum of the e.m.f.s is equal to the sum of the p.d.s.” For example:

  26. Voltage at a point The voltage here is 6V The voltage here is 4.5V The voltage here is 3V The voltage here is 1.5V Take this point as being 0V

  27. Voltage-position graphs 6V 5.9V 4.5V 1.5V 0.1V 0V

  28. Work done V = W Q Voltage = work done charge Definition of a volt: The voltage between two points is the work done per coulomb travelling between the two points We can see that 1V = 1JC-1

  29. Example Questions • A battery does 9J of work. If it transfers 6C of charge what is the battery’s voltage? • A powerpack does 100J of work in transferring 20C of charge. What is the voltage? • A 9V battery transfers 20C of charge. How much work did it do? • If the current of the battery is 0.2A how long was it used for? • 240J of work is done to a 12V motor. How much charge flowed through it? • If this motor was used for 40 seconds how much current did it draw?

  30. Electrical Power Voltage = work done charge 1) Recall: W = QV P = W T 2) Also, recall that power = rate of doing work Power = work done time Power = charge x voltage time P = Q x V T 3) Therefore 4) But I = Q T so Power = current x voltage P = IV

  31. Using voltmeters and ammeters A V The resistance of an ammeter is assumed to be very small – this ammeter will only have a very small voltage across it. The resistance of a voltmeter is assumed to be very large, so only a small current will go through it.

  32. Resistance Resistance is anything that will RESIST a current. It is measured in Ohms, a unit named after me. Georg Simon Ohm 1789-1854 V Resistance = Voltage (in V) (in ) Current (in A) I R The resistance of a component can be calculated using Ohm’s Law:

  33. An example question: Ammeter reads 2A A V Voltmeter reads 10V • What is the resistance across this bulb? • Assuming all the bulbs are the same what is the total resistance in this circuit?

  34. More examples… 3A 3A 2A 4V 2V 1A 6V 12V What is the resistance of these bulbs?

  35. Resistance Resistance (Ohms, ) = Potential Difference (volts, V) Current (amps, A) Resistance is anything that opposes an electric current. • What is the resistance of the following: • A bulb with a voltage of 3V and a current of 1A. • A resistor with a voltage of 12V and a current of 3A • A diode with a voltage of 240V and a current of 40A • A thermistor with a current of 0.5A and a voltage of 10V

  36. Resistors in Series I V1 V2 VT R1 R2 “In a series circuit current stays the same but voltage splits up” VT = V1 + V2 VT = IRT But V1 = IR1 and V2 = IR2 IRT = IR1 + IR2 RT = R1 + R2

  37. Resistors in Parallel IT I1 I2 IT V IT = V RT R1 R2 V = V + V RT R1 R2 1 = 1 + 1 RT R1 R2 “In a parallel circuit voltage stays the same but current splits up” IT = I1 + I2

  38. Example questions Calculate the equivalent resistance: 40Ω 1) 10Ω 2) 20Ω 10Ω 20Ω 100Ω 50Ω 100Ω 3) 4) 20Ω 100Ω 50Ω

  39. Power through a resistor Recall: 1) P = IV 2) V = IR Putting these two equations together gives us: Power = I x IR = I2R or V2/R • A 10Ω resistor has 2A flowing through it. Calculate the power dissipated by the resistor. • A motor takes a current of 10A. If its resistance is 2.2MΩ calculate the power dissipated by the motor. • A 2KW heater has a resistance of 20 Ω. Calculate the current through it.

  40. Carrier Density The diameter of a copper atom is about 0.25nm Consider a copper atom: This means that there will be 1 / 0.25nm = 4 x 109 copper atoms in 1 metre. Theoretically ,in this cube there must be (4 x 109)3 = 6.4 x 1028 copper atoms. Consider a copper cube of sides 1m: Assuming each atom has one free electron there are 6.4 x 1028 free charges per cubic metre – this is called the “charge carrier density” (n)

  41. Some questions… • If, for copper, n = 6.4 x 1028 and each electron has a charge of 1.6 x 10-19C how much free charge was in the cubic metre? • How much free charge would be in 1mm3 instead? • Calculate the carrier density for a cubic metre of another atom with diameter 0.3nm. Assume each atom has one free electron again.

  42. Drift Speed Definition: Drift speed is the speed with which electrons will move down a wire. How do we work it out? Consider a wire of cross sectional area A and charge carrier density n, where each carrier has the charge q and they are moving with a drift speed of v. • Every second the volume of charge carriers that pass a point will be Av • Therefore the number of charge carriers that pass by every second is given by nAv • Therefore the charge that passes by every second will be nAvq • But charge per second IS current, so… I = nAqv

  43. Example questions • Calculate the current down a 1mm2 wire where the drift speed is 1mms-1 and the carrier density is 6.4 x 1028m-3 (remember that the charge on an electron is 1.6 x 10-19C) • Calculate the drift speed down a 2mm2 wire which has a current of 0.5A passing through it and a carrier density of 6.4 x 1028m-3.

  44. This seems slow… Bulb Battery The drift speeds in the previous questions seemed very slow – why is it that when you turn on a light bulb it lights straight away then? Consider the electrons in the wire: When an electron is pushed in it knocks on the others so that electrons “come out” at the other end. Simple really…

  45. Comparing Drift Speeds 1 2 Consider two wires connected in series: Q. The area of wire 2 is twice that of wire 1. Which wire do electrons travel fastest in? In wire 1 I1 = n1A1q1v1 In wire 2 I2 = n2A2q2v2 However, in series I1=I2 therefore n1A1q1v1 = n2A2q2v2 Also, q1 = q2 and n1 = n2… Therefore A1v1 = A2v2

  46. Resistivity Resistance = resistivity x length area R = ρL A The resistance of a wire depends on 3 things: the length of the wire, the width of the wire and what the wire is made of: • Calculate the following: • The resistance of a copper wire of length 2m, area 2mm2 and resistivity 1.7x10-8Ωm • The resistance of an iron wire of length 100m, area 5mm2 and resistivity 1x10-7Ωm • A copper wire has a resistance of 5Ω. If the wire is 20m long and the wire is cylindrical what is the radius of the wire?

  47. Electron Drift Electrons Ions What happens inside a conducting material? The following model of a metal wire could help: At normal temperatures, with no current flowing, electrons hurtle around continuously. They collide with ions but because their movement is random there is no net energy transfer.

  48. Electron Drift Electrons Ions Now apply a voltage: Negative Positive This time we can see that the electrons are accelerated from negative to positive. This movement is superimposed on top of the random velocities and is responsible for electrical effects.

  49. Understanding Current Increasing the temperature of a metal will increase the ___________ of the ions. This will increase the ________ of the metal and decrease the current because it lowers the ____ _____. In semiconductors the carrier density is small but _________ with temperature, so the resistivity of a semiconductor decreases with temperature (e.g. a ________). In insulators n is very low. Recall the equation: I = nAqv Words – thermistor, resistivity, vibrations, drift speed, increases

  50. Potential Dividers VIN R1 VOUT R2 0V 0V The Potential Divider equation: (R2) VOUT VIN x (R1 + R2)

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