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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.

  1. 1
  2. 2
  1. 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
  2. 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
  3. Skill Area P - Planning experimental procedures.

    fieldwork, where variables cannot readily be controlled and to make judgements about the amount of evidence needed in these contexts; h to select apparatus, equipment and techniques, taking account of safety requirements MARK DESCRIPTIONS: The mark descriptions are designed to be hierarchical. 6 marks P.6a Use scientific knowledge and understanding to plan a procedure, to identify key factors to vary, control or take into account, and to make a prediction where appropriate * Produce a plan of how the experiment will be carried out * Say what factors will affect how well the experiment will work.

    • Word count: 3379
  4. To find which of the circuits, shown below, are most suitable to measure a range of resistances, which the meters (the voltmeter and the ammeter) could be used to measure.

    For the smallest resistance = 50? Therefore the range of resistances that these meters can be used to measure is from 50? to 50000?. I will be assuming that the Lab Pack has a negligible internal resistance. The resistance of the Voltmeter calculated from Ohms Law, using the values specified on the device itself is 50000?: = 5 x 104 ? The resistance of the ammeter is as specified on the ammeter itself which is 40?. Prediction for Circuit One: Circuit One as shown in the diagram above as the voltmeter connected in parallel around the resistor only.

    • Word count: 7521
  5. Investigating how temperature affects the resistance in a wire

    This means that despite the driving force/voltage the speed at which the electrons flow through a circuit (ampage) is reduced. This also means that if you increase the voltage you increase the ampage (as long as the resistance is constant). These therefore means that the voltage, ampage and resistance are all connected in some way, the formula for this is: V = I * R I = V / R R = V / I (Where I = the current, R= the resistance, V= the voltage) Resistance is created by the positive ions in the metallic structure, which form obstacles in the path of the current (moving free electrons).

    • Word count: 7665
  6. The aim of my investigation is to determine the specific heat capacity of aluminium.

    The temperature difference between the heating filament and aluminium determines the rate of energy transferred from the heating filament to the block. The apparatus reach equilibrium when both are the same temperature. When the heating filament is placed in contact with the cooler aluminium block the heat will flow towards the cooler object i.e. the aluminium block. This is thermal conduction. Aluminium is made up of a crystalline structure in which the positive metallic ions form a three dimensional lattice.

    • Word count: 5292
  7. Investigating the factors affecting the size of current flowing through a length of resistivity putty.

    For this experiment I will refer to the resistivity of the putty as being 40 m?m (40 micro ohm meters) as this is an easier number to use. PREDICTIONS AND REASONING 1) LENGTH EXPERIMENT I predict that doubling the length of the resistivity putty will halve the amount of current passing through the putty, provided all other factors such as the voltage across the putty remain the same. ie length is inversely proportional to current. This prediction can be explained on two levels.

    • Word count: 7146
  8. Investigating the factors that affect the conductance of a solution

    Before conducting this investigation I knew very little about this field of physics but after doing the research and carrying out the experiments I have learned a much greater insight to the workings of conductance. Method Different concentrations To begin with it was essential that all concentrations of solutions used in the experiment were uncontaminated since this would immediately make the results of the experiment invalid. First collect the required apparatus and set it up as shown in diagram 1.

    • Word count: 3910
  9. The Purpose of my sensing circuit is to regulate the temperature in a Steam Sauna which operates between the temperatures 30C - 60C

    A rise in temperature thus increases the overall conductance of a Negative Temperature Coefficient thermistor. A simple model is shown below At 30°C the NTC thermistor has few mobile charge carriers At 60°C some atoms ionise and increase mobile charge carrier density of the NTC thermistor KEY Potential Divider A potential divider can be made by connecting at least two resistors in series across a source electromotive force in a circuit. In a potential divider circuit the ratio of resistances determines the potential difference across a resistor. The larger the resistance, the greater the potential difference across the resistor and the smaller the resistance the smaller the potential difference across it.

    • Word count: 3975

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