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AS and A Level: Electrical & Thermal Physics
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Doing circuit calculations
To find the total resistance of a circuit follow these steps.
1) Replace any parallel network with a single equivalent resistor, REQ using 1/REQ= 1/R1 + 1/R2.
Tip: REQ will be lower than either of the parallel resistors R1 or R2 so you can check your calculation.
2) Add all of the series resistors together (including REQ) to find the total resistance of the circuit RT.
- 2 Calculate the total circuit current, IT using IT = V/RT. This current flows through all of the series resistors so the p.d. across each series resistor is given by V = IT R. The p.d. across any parallel network will be IT REQ.
- 3 A potential divider circuit consists of two resistors in series. Follow the same steps as above to find the p.d. across each resistor. Alternatively, R1/R2 =V1/V2 or V1 = V *R1/(R1 +R2) [V = supply voltage]
Which bulb is brightest?
1) If two bulbs are in series, they have the same current. The brighter bulb is the one with greatest power, P. Use P = I2R. The bulb with largest R is brightest.
2) If two bulbs are in parallel, they have the same p.d. across them. Use P=V2/R. The bulb with the lowest R has the highest power and is therefore brightest.
- 1 Use the correct units. If diameter is given in mm, convert to metres before calculating area, A. e.g. d = 1mm so r = 0.5mm = 0.5 x 10-3 m. So A = x (0.5 x 10-3)2 = 7.9 x 10-7 m2.
- 2 Typical questions involve proportions such as what happens to R if the diameter of the wire is doubled? Doubling the diameter would double the radius. Doubling the radius would quadruple the area. So the resistance would decrease to ¼ of the original resistance. The same argument explains why a thinner wire has a higher resistance.
Applications of resistivity:
1) A rheostat is a resistor made by winding a wire around a cylindrical tube. A sliding contact changes the length of the wire carrying current and therefore changes the resistance, R.
2) A strain gauge, has a resistance that increases when it is stretched because the wire from which it is made increases in length.
3) The battery tester on the side of some AA batteries works by using a shaped conductor. The thin end has lowest A, therefore highest R. Current is the same at all points, the thin end gets hottest (P = I2R) and a thermochromic ink becomes transparent, revealing a display.
- 1 Many students find internal resistance a difficult concept. However the circuit is similar to a potential divider. Think of the circuit as a cell of emf E, in series with an internal resistance, r and an external resistance R. When current, I flows through the circuit, E = Ir + IR. This is Kirchhoff’s 2nd law.
- 2 Using a voltmeter to measure the terminal p.d. V, we can rewrite the equation E = Ir + IR as E = Ir + V and then rearrange to give V = rI + E which is the equation of a straight line. A graph of V against I gives a straight line of gradient -r and intercept E. This is how to find the emf experimentally.
- 3 When the current through the cell is high, there is a large drop in the terminal p.d. The difference between the cell emf and the terminal p.d. is called the ‘lost volts’ and equals Ir.
- 4 Short circuiting the cell will lead to a large drop in external voltage and large amount of power dissipated in the cell as P = I2r.
- 5 A car battery (lead acid) is designed to supply large currents. When switching on the engine the current is large and there will be a large drop in terminal p.d. and this will cause lights to dim momentarily.
When the wire is lengthened, the journey is considerably longer as the electrons collide with more atoms. The size of the wire should change the amount of resistance in the circuit. In metals, the outside electron is held very weakly by the nucleus, (see fig 1). This is particular to metals only. When a charge is applied to the wire, the atoms will move in the electronic current. When the wire is heated, the metal atoms will move about, making it difficult for the electrons to pas through, therefore increasing the resistance.
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It will also give clear and concise readings that can be trusted and used for comparing/observing trends. I chose not to measure the width of the wire and presume that the wire is of the stated thickness of 28 swg Nichrome wire. For this experiment I will assume that the wire is perfectly round at 0.38mm diameter. FORMULA'S Charge is measured in coulombs and charge is the amount of current that flows every second. Electric current is measured in AMP's (A), Charge in COULOMBS (C)
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As a result, my prediction is that as the light intensity increases, the voltage output will decrease. Methodology The investigation will be carried out in the laboratory. This is so that external factors - except for the independent variable - remain relatively constant. Such factors that need to be controlled include the temperature of components and humidity of external environment, although the Wheatstone Bridge arrangement already overcomes these. I will take a range of seven values between 0 lux and 60 lux.
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Variables Any Indirect light coming from another light source could affect the experiment. Wire temperature causing an increase in resistance Apparatus I will use two digital meters set on 200mA and 2mV range that will allow results to be measured to the nearest 1mA and 1mV respectively. Also a resistance box will be set on a resistance of 50? to try and keep the resistance level during the experiment. A standard lamp powered by mains electricity with a 60W bulb will be used as a light source.
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491 0.000436 0.491 2290 428 529 0.000428 0.529 2340 422 555 0.000422 0.555 2370 414 601 0.000414 0.601 2420 412 621 0.000412 0.621 2430 406 644 0.000406 0.644 2460 397 711 0.000397 0.711 2520 390 760 0.000390 0.760 2560 384 809 0.000384 0.809 2600 378 854 0.000378 0.854 2650 364 956 0.000364 0.956 2750 360 995 0.000360 0.995 2780 346 1114 0.000346 1.114 2890 340 1161 0.000340 1.161 2940 Calculating the power output of the photovoltaic cell: Power (W) = Current (A)
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This then allows you to work out the angular velocity of the motor at different tensions. The torque can be calculated by multiplying the weight at the end of the string (which equals the tension of the string) by the radius of the motor. The experiment would then be repeated with a variety of different weights. The apparatus and how it is set out can be seen in the diagram above. Method 2 Method 2 is on a smaller scale, and involves a motor being held in place on a bench with a leather strap being wrapped around it and attached on either end to a Newton meter.
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* Tape and glue (stick stuff together) * 2 small wood pieces (to support the axel at either end) * Electric hand drill (spin the generator) * Galvanometer (test the current) METHOD 1. Construct all the parts together as in the diagram below. 2. Make a hole in the middle of the cylinder shape wood piece and put the axel through that hole (the wood piece should be near the end of the axel as seen in the diagram below). Glue the ends so it doesn't move (see diagram). 3. Wrap 50 times around the wooded piece (armature) the insulated copper wire and hold it in place with the tape or glue (see diagram).
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and the output I shall measure will be the potential difference across the LDR. The equipment I shall need for the initial experiment is as follows: * LDR * Light source (bulb) * Powerpack * Multimeter (used as an ohmmeter) * Wires The multimeter will be set to measure resistance. The alternative to using a powerpack is to use a battery pack. However, from experience and my own knowledge I know that the 6V battery pack is insufficient to cause the bulb to light due to high internal resistance, so not enough voltage to power the bulb.
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Since a Polaroid plane polarises the wave, I will be able to use that. Unfortunately, this has the effect of halving the intensity of the light; increasing the need for a more sensitive resistor. There were two other methods I considered: Lasers are already polarised, so I could have used a laser to pass through a rotating Polaroid. However, the problem with this is that although I am not losing any of the original light by passing it through a Polaroid, the laser's initial intensity is much lower than the intensity of the original light bulb.
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Other variables include thickness of wire, which is a variable as it increases the surface area that the wire process and different types of wire which could effect the experiment as they might have a different atomic make up than others. To insure I get adequate range of data I believe that it is necessary to make the length of wire that I am testing about 200 cm as this allows me to carry out the experiment for such a length of time that I can make sure that there is no anomalies present in the data I have collected.
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The thickness of the wire would also affect the resistance of wire, a thick wire of the same material, length and temperature would have less of a resistance of a thinner wire, this is because there is more room for more electrons to be able squeeze together, creating more 'lanes' for the electrons to be able to pass through, this increases the current, which for if the voltage was the same, would lower the resistance, we can see this using the simple formula: Where V is voltage and I is current.
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Plan: Circuit - Explanation - The water is boiled until it reaches a temperature of just above 90� Celsius. The thermistor is inserted into the hot water and the voltage across it is measured for a temperature of 90�. The varying voltage across the thermistor is measured as the temperature falls at 10-degree intervals. The experiment is repeated and a second set of readings obtained. An average set of readings is obtained and a voltage-temperature conversion graph is plotted. Then test the sensor by attaching the amplifier and relay. Materials/Apparatus Needed: Thermometer, Thermistor, Beaker, Electric kettle, Power supply, Multimeter, Variable resistor, Amplifier, Relay, Leads.
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Talk about Silicon picture on board (crystalline type) Slide 3 Here are the contents of my presentation. Slide 4 Carbon, silicon and germanium (germanium, like silicon, is also a semiconductor) have a unique property in their electron structure -- each has four electrons in its outer orbital. This allows them to form nice crystals. The four electrons form perfect covalent bonds with four neighbouring atoms, creating a lattice. In carbon, we know the crystalline form as diamond. In silicon, the crystalline form is a silvery, metallic-looking substance.
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thermistor. If the sign is negative, the resistance decreases as the temperature increases. This is called a negative temperature coefficient (NTC) thermistor. VARIABLES For my experiment to be a success I must make it a fair test. To do this there are some factors I need to keep the same and some I need to change. The main factor which will be changed is the temperature of the water so I can determine the resistance of the different temperatures. However, there are a few things which I will keep the same. I will need to keep the thermistor and resistor I use the same. This will ensure that my readings are more accurate.
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The temperature of the water was also noted at each voltage. The temperature of the water may change as the heat energy emitted by the bulb is absorbed by the water. The light energy is very small and hence is difficult to measure it directly. So it shall be measured it by subtracting the heat energy given out from the total input energy. The light bulb is submerged in 0.2kg water, and turned on for 900 seconds. The current and voltage of the electrical supply is noted and a table is made with initial findings.
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The limited amount of types of wires will not allow me to have enough readings and therefore restrict the range of my results. I have decided not to investigate the resistance of a wire by varying the cross sectional area as it is extremely difficult to measure the diameter of a wire accurately with the given equipment. However, the widths of the wires are given to us on the packaging. It is written as SWG (Standard Width Gage) and the higher the number, the thinner the wire.
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I chose this because it is the most practical to carry out within the laboratory. Not a lot of equipment is needed and it can be controlled without complications as I would have to use one wire and just keep changing the length by connecting one end of the circuit to the wire at the length required. It will also produce reliable results where trends can be observed easily. Had I chosen any other variable, for example the diameter (or cross-sectional area) I would have had to use wires of different diameter, this can be very expensive and impractical.
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Data Collection Conditions: 5 volts, 220,000 ohms, starting at 1800 nC Number of Tapping Charge (nC) � 1 (1st try) Charge (nC) � 1 (2nd try) 1 1644 1721 2 1144 1234 3 837 850 4 597 597 5 406 427 6 326 307 7 236 205 8 168 122 9 119 95 10 84 67 11 56 50 12 39 37 13 24 25 14 16 17 15 10 10 16 6 6 17 5 4 18 3 3 29 2 2 20 0 0 Data Processing Using Logger Pro, we determined the rate of discharge, by drawing a curve of best fit.
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It has a spring attachment hole at one end and a mechano shaft for attaching weights > Expendable Spring, an attachment unit to keep the rotating apparatus together, and the main unit holding weight of equipment > Digital Multimeter, for measuring voltage differences > Wires, for construction of circuit > Weights, each weighing a mass of 10 grams > Clamp stand, to ensure the potentiometer is stabilised and attaches the spring > 360� Protractor, to measure the angle of rotation done by the MDF wheel Circuit Diagram: Safety Working with 6v is relatively safe; the only caution is to ensure wires are making minimal contact to prevent shorting of the circuit.
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up as below However because the power supply has an internal resistance the diagram could be drawn like this instead What is displayed in the red circle is actual one single thing: the power source, or in my case the battery. However it can be drawn as two separate items for illustration purposes. It represents a 'perfect cell' of e.m.f. (E) with a separate resistor, but in actual fact it is all one item. R and r are in series with each other, they therefore have a combined resistance of R + r, therefore we can write the equation E = I(R + r)
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They are more expensive to buy but last up to two thousand hours. They can be either 240V bulbs, which are usually tubular and often used in up lighters and outdoor floodlights, or low voltage bulbs typically used in down lighting. All halogen lamps require special light fittings. Advantages: Low voltage halogen lamps are slightly more efficient than normal bulbs of the same wattage, but they use a transformer that can consume from 10 to 30 percent of the bulb energy, reducing the efficiency gain. More efficient electronic transformers are available which reduce transformer losses.
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Aim To build and test a temperature sensor and analysing its suitability as a bath water thermometer.
These can be used as current limiters or in place of a fuse. Current through the device causes some resistive heating. If the current is too large the resistance increases due to heat increase and the current is reduced. * The negative temperature coefficient thermistor or NTC thermistor has a decreased resistance as temperature increases. Deciding on which of these to use in my circuit isn't a problem because both will change with temperature change just one has its resistance changed opposite to the other in temperature change.
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With the numbers showing faster than the human eye can see to choose them. Therefore making it impossible to choose numbers. So it must count faster than .. I will research this later... Must operate from a 9V battery, as these are commonly available. Must consume as little power as possible, otherwise battery life will be short. So have current consumption of less than 200mA. Possible Solutions: My specification can be achieved in a few ways... I) A button is pressed, which triggers 7 numbers each on there own 7 seg display. Each number would have to be own timed.
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To make this a fair test I will be working at room temperature, which should be approximately constant. Safety There are no serious safety precautions for this experiment, however, I will make sure that the voltage does not exceed 10-12V as this may cause the Meyer Lamp to blow. Accuracy I will carry out the experiment three times so no obvious mistakes will be made. The accuracy with which I can determine the current depends on how many significant figures the ammeter will read them to.
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Ways to measure temperature. Ways to measure temperature can include; * A thermocouple * A thermistor * Wheatstone bridge * A Resistance temperature Detector (RTD) A thermocouple uses two pieces of dissimilar metals that have a contact potential between them, and this contact potential changes as the temperature changes. The problem with using a thermocouple is that the output voltage is typically a few micro volts per �C. Normally, the output of thermocouples is amplified using an operational amplifier (op-amp)
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