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AS and A Level: Electrical & Thermal Physics

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Doing circuit calculations

  1. 1 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. 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. 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]
  4. 4 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.

Resistivity

  1. 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. 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.
  3. 3 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.

Internal resistance

  1. 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. 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. 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. 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. 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.

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  1. Objective: l To rectify an a.c. signal using a half-wave rectifying circuit. l To rectify an a.c. signal using a full-wave rectifying circuit. To smooth a full-wave rectified a.c. signal using a smoothing circuit.

    form for proper operation. Therefore, diodes are used to rectify the circuit. Half-wave Rectification (Figure C25.1) If one diode is used, only half of the a.c. signal is allowed to get to the load. For the first half of the a.c. cycle, the diode is in forward bias, so there is a current flowing through the diode and the resistor. For the second half of the a.c. cycle, the diode is in reverse bias, so there is no current flowing through the diode and the resistor. As only half of the a.c. cycle is used, so it is called half-wave rectification.

    • Word count: 1769
  2. A. Study of phase difference between voltage and current in series RC and LR circuit B. Study of resonant frequency in parallel LC circuit

    (in phase) B. RL circuit After connecting the RL circuit, turning on the low voltage a.c.power supply and setting it to 2V and 50Hz, the traces shown on the CRO was observed and sketched. 1100-turn coil with resistance 2.2k?: � The phase difference between the voltage and the current was about 0 rad. (in phase) 1100-turn coil with resistance 100?: � The phase difference between the voltage and the current was about?/2 rad. The voltage leads the current by ?/2 rad.

    • Word count: 1296
  3. Study of capacitors in charging And discharging processes 1

    Investigation of factors affecting charging and discharging Part A and B were repeated with the other capacitors (100�F, 220�F, 470�F, 1000�F) by using a 6V battery ( 4 x 1.5V). The readings of the galvanometer were observed and recorded, and then tabulated below. Capacitance (C)/�F 100 220 470 1000 Current (I)/mA 2.00 3.14 4.57 6.00 The steps were repeated with the other voltages (1.5 V, 3.0V, 4.5V and 6.0V) by using a 470�F capacitor. The readings of the galvanometer were observed and recorded, and then tabulated below.

    • Word count: 1030
  4. Investigating the relationship between pressure, volume and temperature of a gas

    The capillary tube is immersed in a water bath of variable temperature. At equilibrium, the pressure of the trapped air is equal to the sum of the pressure due to the weight of the mercury thread PHg and the pressure due to atmosphere Patm. Both PHg and Patm are independent of the trapped air which, hence, is conditioned to change its volume and temperature at constant pressure. (II) P-T at constant V To establish a constant volume environment while allowing pressure and temperature to change, a round-bottomed flask is used to contain a certain amount of air, and immersed in a water bath of variable temperature.

    • Word count: 1455
  5. Plotting equipotential lines of electric field

    Two points B. Point and line C. Two parallel lines Disscusion: 1. The role of the conducting plate The conducting plate has nearly zero resistance. When the plate is connected to the power supply by using electrodes, the plate then conducts electricity and has electric field. It provides a surface for us to test the potential difference within the plate by using flying probe. So the equipotential line could be found easily. 2. Comparing the equipotential line patterns with the electric field patterns in Part A of Experiment C3 Experiment C3 is sprinkling semolina powder onto the non-conducting oil in an electric field.

    • Word count: 817
  6. Finding the Resistivity of a Wire

    Next I will fix the wire to the ruler. I will start by tightly fixing one end of the wire to one end of the ruler using sticky tape. Then I will ensure the wire is straight and tight before fixing it at a point approximately 0.35m down the ruler. I will repeat this at 0.65m and at the end of the metre ruler. Subsequently, I will connect the circuit as shown in the diagram, with the wire connected between 1.00m and 0.00m.

    • Word count: 2530
  7. Making, Calibrating and Testing a Sensor

    Then as the car drives through the garage the LDR will sense how close the car is by sensing how much light is hitting the LDR. The more light reaching the LDR, the further away the car is. Once the car has reached the maximum point it can safely park a buzzer will sound and the driver should park his vehicle. The circuit will be used on experiments to select a resistor for optimum sensitivity, calibrate the LDR's operation and measure the resolution of the sensing circuit.

    • Word count: 1961
  8. The potato - a source of EMF

    What is EMF? EMF is the electrical pressure that pushes current around the circuit and is measured in Volts. Although EMF is measured in Volts it is not the same as Potential difference, which is the electrical pressure difference across an electrical component. Some of the energy given by the potato cell is used up in the cell itself through having to push the electrons through the system; this is called internal resistance. I imagine that the greater the distance between the two electrodes the greater the internal resistance as more energy will be needed to push the electrons a further distance through the system.

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  9. Magnesium Diboride

    The majority of superconductors similar to MgB2 have a critical temperature of -269�C, or about 4 Kelvin. Now, a difference of 35 degrees might not seem to be of much consequence, especially when dealing with such extreme temperatures, but because you're dealing with such low temperatures, those 35 degrees make the difference between using liquid helium (a very difficult and volatile substance to work with) and electrical closed-cycle refrigeration (a much less expensive system3). Diamagnetism is a form of magnetism that is only present when a material is put under an external magnetic field. When a magnetic field is applied to a substance, it changes the orbital motion of the electrons; this change is signified by the

    • Word count: 903
  10. Investigation into the resistance of a filament lamp

    As the temperature of the filament changes the resistance also changes. Problem Identified I have decided to investigate into the resistance of a filament lamp. I will measure the current and potential difference of the filament lamp at various points, after measuring current and potential difference I will draw a graph to show the relationship between current and potential difference. By finding 1 over gradient of the I/V characteristic graph we can work out the resistance of the filament lamp.

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  11. Investigating Internal Resistance

    The main variable in this experiment is the external resistance. As the external resistance increases the voltage will decrease. This is because fewer electrons can pass, also this increase in resistance will cause an increase in current. Measurements: In this investigation the voltage and current levels as resistance changes will be recorded. The results for each resistance will be recorded 3 times for both voltage and current to improve accuracy. These results will also be recorded to a two decimal place degree of accuracy. Apparatus...in detail: Power pack: The power pack used was the same throughout.

    • Word count: 2097
  12. Experiment to investigate how the resistance of a strain gauge attached to a piece of wood varies with the temperature of the wood.

    To measure the temperature of the wooden block, I shall use 2 thermocouple devices , one of which I shall attach to the wooden block by using a substance called araldite 2024, which has a good thermal conductivity and a high melting point. ref1. I will use general purpose thermocouples as they can be used to measure high temperatures and are responsive enough to a temperature of 400�C. The ranges of temperature that I will be using are 0�C to 40 �, as these are the extremes the temperatures are likely to be in an average household.

    • Word count: 554
  13. An experiment to measure the specific heat capacity of water

    = less risk of uneven heating We considered that less water and less time to achieve the maximum temperature would provide a diminished range of readings which could potentially decrease our accuracy but felt that the reduced risk of errors from using a smaller beaker outweighed this risk. We therefore decided to use a beaker of even smaller volume. We proceeded to insulate this beaker with two layers of bubble wrap and 2 layers of felt and then placed the beaker on a further to layers of bubble wrap as an extra precaution to prevent heat loss errors.

    • Word count: 1335
  14. An Investigation into how electrons move

    We were however advised that the size of the crystal would not affect the experiment and so we considered that this potential source of error may be negligible. We recorded all of our measurements which are shown below. We felt that we could improve our accuracy further by performing a couple of trial experiments to see how we could improve upon our initial ideas. In our trial, we used a distance of 3.08cm and a voltage of 100v. We discovered that the crystal moved extremely slowly.

    • Word count: 1958
  15. eletrical dc motors

    The rotor consists of windings (generally on a core), the windings being electrically connected to the commutator. The above diagram shows a common motor layout, with the rotor inside the stator (field) magnets. b) Windings: The DC machine armature windings are always of the closed continuous type of double-layer lap or wave winding. For small machines, the coils are directly wound into the armature slots using automatic winders. In large machines, the coils are preformed and then inserted into the armature slots. Each coil consists of a number of turns of wire, each turn taped and insulated from the other turns and form the rotor slot.

    • Word count: 1330
  16. investigating the relationship between the diameter and the current in a wire at its melting point

    The Resistance should be directly proportional to All of the variables will be measured or known. Method Preliminary experiment Determine a length for the Wire The longer the length of wire the larger the resistance. Therefore a longer wire will make it easier to measure changes in current and voltage. However wires longer than 1 metre need to be measured using 2 meter rule sticks put together. This increases the uncertainty and is more difficult to measure; therefore I will use 1 metre pieces of wire as this length can be measured easily with smaller uncertainties and is still of a sufficient length.

    • Word count: 1907
  17. investigating the relationship between the diameter and the current in a wire at its melting point

    A = Cross sectional area ? = Pie D = Diameter (http://www.equationsheet.com/sheets/Equations-20.html) So putting these formula together- A = ? 2 And R = ? . l A R = ? . l ? (d/2)2 R = ? . l ? . d2/4 R = 4 . ? . l ? . d2 R = 4 . ? . l . 1 ? d2 R = 4 . ? . l . 1 + 0 ? d2 Y = m x +c References to the specification - Aim Of My Investigation - The aim of my investigation is to investigate the relationship between resistance and cross sectional area of a wire.

    • Word count: 1678
  18. Sensors cwk. The aim of this coursework is to construct a potential divider circuit with a light dependent resistor (LDR), and observe how light intensity affects the voltage output

    and the resistance decreases as the brightness of light falling on the LDR increases. There are two main types of light dependent resistors, the negative co-efficient, which causes the resistance of the device to fall as the light falling onto it increases. Whereas, some other LDR's work in the opposite way i.e. their resistance increases with light, called positive co-efficient LDR's. For, the purpose of this coursework we are only going to need to now about the negative co-efficient. If light falling on the negative co-efficient device, is of a high enough frequency, photons absorbed by the semiconductor gives bound electrons enough energy to jump into the conduction band.

    • Word count: 4605
  19. Free essay

    Finding the internal resistance of a solar cell

    Variables: During this experiment I have noticed that there will be conditions that are variable and conditions that are not variable. Considerations of these conditions must be made. The conditions which must remain constant are the amount of light energy which the solar cell receives as this may affect the internal resistance of itself so must remain constant as to not affect the results. This can be solved by making sure a constant light source such as a lamp remains at a set distance from the solar cell.

    • Word count: 1879
  20. Physics - Sensor Project

    Also with the problem of limitation of apparatus for my experiment it shall limit me to how and what I would like to do for my sensor. http://img2.timeinc.net/toh/i/a/plumbing/leaky-toilets-02.jpg Potential Divider Potential dividers are used in circuits to divide the voltage across a line in the circuit. They are generally used is circuits which require calibration or adjustments of voltage across components in the circuit. For example when a voltage of 6V is required across a circuit generally a 9V battery is needed, to achieve the 6V the only option that can be used is a potential divider.

    • Word count: 1476
  21. Physics industrial visit

    Although the initial costs are high the system is incredible in the way it increases the efficiency as the amount of power per amp for example a standard single phase 120/240 volt supply at 100amps would provide around 18000-26000 watts whereas a three phase supply with the same supply could provide up to twice as much. So when you look into this it means that the same amount of power can be generated with a lower voltage meaning less electricity is required which will therefore reduce the running costs of the tram.

    • Word count: 1299
  22. A2 Viscosity investigation

    (ensure the first line is at least 3cm from the top of where the syrup is filled to as it needs time to reach terminal velocity) 4. Place the ball bearing into the syrup then get to eye level of the first line to ensure maximum accuracy and then start the timer when the bottom of the ball bearing touches the line previously drawn. 5. Kneel until you are at eye level of the second line and wait until the bottom of the ball bearing touches the line and stop the timer.

    • Word count: 2351
  23. Investigating the Smoothing Effect of a Capacitor on a Resistive Load

    1.2 100 0.05 6.0 6.0 0.300 0.255 100 1.2 100 0.05 3.4 3.4 0.170 0.120 220 1.2 100 0.01 7.5 7.5 0.075 0.055 470 1.2 100 0.005 6.3 6.3 0.031 0.026 1000 1.2 100 0.005 3.0 3.0 0.015 0.012 The experiment was repeated and more readings recorded in order to diminish the possibility of anomalies and errors occurring and to obtain more reliable results. Problems encountered Using the oscilloscope required us to ensure that the trace that appeared on the screen would be appropriate to read from and to calculate such values as the frequency.

    • Word count: 2664
  24. resistivity if a nichrome wire

    1 Nails N/A N/A I will use these to hold the nichrome wire to the meter stick. 2 Dependant and independent variables Independent variable- The independent variable throughout this investigation will be the length of the nichrome wire. I will change the lengths to determine the voltage for each length. These results will therefore aid me in resolving what the resistance in the wire is. Controlled variables All there variables must stay constant in order to prevent them from affecting the dependant variables, and therefore creating anomalous results. What to be kept constant Why is it kept constant How it's going to be kept constant.

    • Word count: 4333

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