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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.


  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. Investigate the resistance if 12 volt bulb when the current changes.

    o Leads Method: 1. Using the apparatus listed above I will set up the following circuit: Key Variable resistor Ammeter Lamp Voltmeter Battery pack Lead 2. I will do a preliminary test to find the range of current in amps. I will do this by moving the variable resistor to its lowest and highest points and noting down the amps. In this case the lowest point is 0.5 and the highest is 1.6 amps. 3. I will start with 0.5 amps, working systematically, I will note down the voltage every 0.1 amps.

    • Word count: 1007
  2. Do we have to learn to think scientifically in order to understand the world?

    "Empirical evidence is evidence that one can see, hear, touch, taste, or smell; it is evidence that is susceptible to one's senses. Empirical evidence is important because it is evidence that others besides yourself can experience, and it is repeatable, so empirical evidence can be checked by yourself and others after knowledge claims are made by an individual.III" We know that logical reasoning is reasoning that is based on pure facts and is not affected by emotions (e.g. hope, will etc.)

    • Word count: 1423
  3. How the resistance of a thermistor changes with temperature keeping the current constant and recording the voltage as the temperature changes.

    Prediction After research of this science I have found that the thermistor is made from a semi-conductible material which we have been told is an NTC ( negative temperature coefficient). In this case I believe that as the temperature increases the resistance will decrease as more electrons are freed and the material becomes a better conductor. The graph produced at the end of this experiment should therefore look like this: Preliminary Experiment Before the main experiment is carried out a preliminary experiment is needed to clarify several problems such as equipment choices and temperature ranges.

    • Word count: 1296
  4. Electrical Resonance - Research and rationale.

    If the capacitance and inductance are connected in parallel, the opposite occurs: the impedance is extremely high and little current will pass. [1] Figure 1:Simple resonating circuit Resonant circuits are used in electrical equipment, such as filters, to select or reject currents of specific frequencies. Filters in which either the capacitance or the inductance of the circuit can be varied are used to tune radio and television receivers to the frequency of the transmitting station so that the receiver will accept that frequency and reject others.

    • Word count: 1408
  5. Characteristics of Ohmic and Non Ohmic Conductors.

    The free electrons are those electrons that are transferred from a positive to a negatively charged ion. This is called the free electron theory. Electricity is basically the transfer of electrons from one atom to the other. In conductors, the atoms are moving in different directions. But when the potential difference is applied between the ends of the conductor, the atoms line up and move to one direction. Electric conductivity means that a certain substance can carry an electric current. Current is a flow of electrons. So the material that can conduct electricity has to have free electrons to carry this current.

    • Word count: 7032
  6. Does a light bulb obey Ohms law.

    It has to be placed in series on the circuit. Voltmeter: This is a device for measuring the potential difference of the electrons in the circuit. They are measured in Volts and it is placed in parallel. Hypothesis: I think that the filament light bulb will not follow ohms law because if the temperature of the bulb increases then the resistance will increase. Ohms law is only true if the resistance stays the same Plan: In my experiment I am going to make a circuit containing the following equipment: * 1 Ammeter * 1 Voltmeter * 1 Power Pack * Wires * 1 Bulb I will put together the circuit by using the equipment I mentioned before.

    • Word count: 917
  7. The strength of an electromagnet.

    Scientific background. When a current flows along a wire, it induced a magnetic field around the wire. The magnetic field occurs at a right angle to the direction in which the current flows. The magnetic field can be made visible by using iron-filings on a piece of paper, with the wire going through he paper. When a current flows along the wire, circles of magnetic field can be seen on the paper, made out of iron-filings. If you wind more than 1 turn of wire, then the effect is increased.

    • Word count: 2423
  8. Factors Affecting The Heating Effect Of A Current.

    and equals an energy transfer rate of 1 joule per second, i.e. 1W = 1J s-1. In the expression P=IV, P will be in watts if I is in amperes and V in volts. A larger unit is the kilowatt (kW) which equals 1000 watts. If all the electrical energy is transformed into heat by the device it is called a 'passive' resistor and the rate of production of heat will also be called IV. The resistance is R. P = IV = V R V� R = I IR = I�R So P = IV = I�R There are

    • Word count: 1392
  9. A capacitance meter.

    The time during which the output is either high or low is determined by the two resistors and a capacitor, which are externally connected to the 555 timer. (3) If the frequency of the clock pulse generator is to be 100HZ and I needed to work out the time, I will calculate it by doing this: T = 1?F T = 1/100 T = 0.01secs (4) If the mark to space ratio (or duty cycle) for the astable is to be 9:1 and I had to work out: a)

    • Word count: 1020
  10. Can A Thermistor Be Used As A Thermometer?

    will change the amount of resistance the thermistor presents.And all other variables, such as amount of batteries, will be kept the same. Our method, based on our research, is as follows: 1. Set up the equipment as shown in the below diagram; 2.

    • Word count: 350
  11. My aim is to find out by changing the depth of the copper changes the current.

    The experiment carried out aimed to monitor if by changing the depth the Copper (Cu) metal in the Copper Sulphate solution (CuSo4) affected the current. Whilst at the same keeping all the above variables at a constant level making the test accurate to find out my aim. I predict that having the copper in the solution will make the current higher when the depth is greater. I think this because more area of copper is exposed to the solution. At 1cm it there is less copper actually in the solution therefore less current is needed.

    • Word count: 911
  12. How a filament light bulb effects current and voltage.

    Voltmeter Ammeter This is the second diagram of the second test, this has the filament light bulb in, this contains: Power pack Filament light bulb Voltmeter Ammeter Variable resistor Safety As always when conducting any experiments coats and excess equipment must be safety out of reach under tables or in cupboards away from the working area. Make sure that no water comes into contact with electrical equipment and hands are dry ro prevent possible electrocution. Method: 1Collect all the equipment- wires, power pack etc 2Set the equipment up shown in the diagrams 3Turn the power pack on and take the

    • Word count: 1029
  13. Resistance is a measure of how hard it is to get a current through a component at a particular potential difference or voltage.

    This is because their will be less of a resistance stopping the electrical current getting through. I also think also think my prediction is correct because components resist the flow of current through them. They have resistance. The greater the resistance of a component or component means the smaller that flows for a particular voltage or the greater the voltage needed to maintain a particular circuit. Plan: I plan to find out in the experiment how the length of bare resistance wire effects the resistance while doing the experiment. To do this I plan to set up a circuit as shown in my diagram and then adjust the resistance wire to different lengths to see if the results are effected by this.

    • Word count: 1010
  14. Electronic Components.

    OR gate Electronic logic gates are digital components that have no in-between states. In multi-input devices they decide outputs. An OR gate gives a positive signal when either or both inputs are positive. AND gate An AND gate gives a positive signal when both inputs are positive. NOT gate A NOT gate gives a positive signal when neither input is positive. Diode Diodes are semi-conductor devices that allow the current to flow in one direction only. Output Components Name How it works Lamp A lamp is a device that converts electrical energy to light as well as a little heat.

    • Word count: 2669
  15. Organisational Change.

    Most emphasis on change results in problems that a manager may face, but considerations should also be given to behavioural patterns that may manifest as a result of resistance. Kanter (1983) observed that in many occurrences the behaviour of managers causes a suppressing effect, rather an encouraging one. O'Day (1978) identified a series of practices whereby managers may seek to discourage subordinates with proposition of change. He called these intimidation rituals, and they include (in order of execution); Nullification, Isolation, Defamation and Expulsion.

    • Word count: 547
  16. The Effects of Temperature on Resistance.

    Thermistor Apparatus * Negative temperature coefficient thermistor. * Voltage meter (V) * Ammeter (A) * Power Pack (Low voltage DC) * Freezer * Heater * Beaker * Thermometer Diagram The Variables In this section I will look at all the possible variables and decide which ones should be varied in order to obtain results showing the effect of temperature on resistance. In the circuit above there are several different aspects that can be controlled and hence be variables. The Voltage: The voltage in this circuit can be changed to an value needed.

    • Word count: 1233
  17. Single Phase Transformer (Experiment) Report.

    for distribution to industrial consumers and finally to 230V for domestic purposes. Power system transformers are usually 3-phase devices, but their basic concepts are most easily demonstrated using a single-phase transformer. Transformers change voltage through electromagnetic induction; i.e. as the magnetic lines of force (flux lines) build up and collapse with the changes in current passing through the primary coil, current is induced in another coil, called the secondary. The secondary voltage is calculated by multiplying the primary voltage by the ratio of the number of turns in the secondary coil to the number of turns in the primary coil, a quantity called the turns ratio.

    • Word count: 3561
  18. In This Investigation, I am trying to find out what affects the strength of an electromagnet. I will do this by carrying out two separate experiments. These will involve changing one aspect of each experiment, whilst keeping all others the same.

    When a strong current is put through the metal, all the domains become free, all facing the same way, able to attract towards other metals Prediction I predict that the more coils that are wrapped round the nail, the stronger the magnetism will become. I think it will be affected less by the amount of current passing through the nail. I predict that the more current that passes through the nail, the more domains will line up in the direction of the current.

    • Word count: 1257
  19. To investigate how the temperature affects the resistance of a thermistor.

    The voltage in a circuit gives the electrons the energy to move and as more voltage is applied and the potential difference across the atoms increases it gives the atoms that are not in the outer shells the energy to push against the force from the nucleus and effectively jump into the band of moving electrons in the outer shells. This applies to the band theory which explains why metals conduct electricity so easy, why insulators conduct virtually no electricity whatsoever and the behaviour of a thermistor.

    • Word count: 3302
  20. The aim of this investigation is to find out if the length of an electrical resistor (graphite putty) affects its resistance.

    Halving the length of the resistor would halve the number of atoms in the substance resulting in half the number of collisions; therefore the resistance is halved. This proportional relationship between the resistance and the length can be shown as in Graph 1: Graph 1: Resistance against length of a resistor Plan: To find out how the resistance of a resistor is affected by its length, we shall set up a circuit. The resistor we shall use is a putty-like substance made of graphite (a form of carbon), which is a conductor of electricity.

    • Word count: 3318
  21. To prove ohms' law, and to study the relationship between current and potential difference (voltage).

    Current (A) Voltage (v) 0.18 1.80 0.20 2.06 0.22 2.23 0.24 2.46 0.26 2.67 0.28 2.95 0.30 3.19 0.39 3.99 * Table of results for two resistors in series of 10? + 12 ? = 22? Current (A) Voltage (v) 0.14 3.10 0.15 3.27 0.16 3.43 0.17 3.65 0.18 3.92 0.19 4.20 0.20 4.35 * Table of results of two resistors of 10 ? and 12 ? in parallel 1/Rtot. = 1/R1 + 1/R2 = 5.5? Current (A) Voltage (v)

    • Word count: 1246
  22. I have decided to choose and investigate; "exploring the characteristics of a sensor."

    I have chosen this sensor as I think it can be used in several different experiments and can be performed straightforwardly and is less complex with standard apparatus. Once I have decided on a sensor I now need to decide on what characteristic I can explore. I have decided to see how the distance away from the light source to the LDR affects the resistance. By doing so I can set up a simple but affective experiment which will give me accurate results to make calculations with.

    • Word count: 1614
  23. Temperature coefficient resistance of a thermistor.

    Apparatus: For this experiment I will need: * A thermistor * A beaker (containing water) * A tripod, gauze and Bunsen burner * Two lengths of wire * A thermometer * A multi-meter set to measure resistance Method: First fill the beaker with water and place over the Bunsen (on a tripod and gauze) and place in it the thermometer and thermister (and shown in the diagram below). Connect the thermistor to a multi-meter and set it to measure the resistance. As the water is heated record the temperature and resistance at different intervals. Results table: temperature resistance temperature resistance 18 571 69 129 21 520 71 119 24 473 74 110 27 448 77

    • Word count: 670
  24. Circuit 31 – Dry sensor (Transistor).

    Thus the LED is unlit. If more than 0.6V is applied to the base, the transistor switches on. Now current can pass easily from the collector to the emitter, so current can flow from the top rail, through R1, the LED and the transistor, back to the battery. The LED is now lit. Resistance of the probes Resistance of the probes will be referred to as RP. In dry conditions resistance RP will be extremely high, whereas in moist conditions resistance RP be relatively low. Consider the variable resistor (VR1) and RP in series.

    • Word count: 556
  25. Intensity on the power output of a solar cell.

    When light hits the cell a certain amount of it is absorbed within this semiconductor. This means that the energy of the absorbed light is also transferred to the semiconductor. The light energy, in the form of photons, knocks electrons loose, allowing them to flow freely. The process is known as the photovoltaic effect. This flow of electrons is a current (I = dQ/dt = rate of flow of charge). By placing metal contacts on the cell, this current can be drawn off in order to power various devices, for example a calculator. An atom of silicon has fourteen electrons, arranged in three shells.

    • Word count: 3282

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