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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. The Resolving Power Of The Eye

    Another important factor is the intensity of both the light being viewed and the background light. Changing light intensity will cause the diameter of the pupil to change and errors to occur, also if background light is brighter than that being viewed it makes it more difficult to see the object or image. For these reasons the experiment must be carried out in a constant darkness with unchanging intensity of the light being viewed. The darker the better as this will give a larger pupil and better resolving power.

    • Word count: 2148
  2. Investigating into factors that effect the Current along a certain length of wire

    I (Current in Amps) = V (Potential Difference Volts) x R (Resistance in ohms) Experimental method: The apparatus was set up as shown above. The apparatus contained what is shown however it can be put in more detail. There would've need to have been a lab with electrical sockets to power the pack. With the length of resistance wire, it must be much more detailed. There are many different widths of wire that are recorded in SWG, as any other units would be impractical. I have chosen to use a 32 SWG for my main wire, however I feel it suitable to use another wire to acts as a comparison.

    • Word count: 2330
  3. Sensor Project

    In electrical terms, materials are classed as either conductors or insulators or semiconductors. Semiconductors are solid materials with conductivities in between the very high conductivity of metals and the very low conductivities of insulators. There are a variety of types of semiconductor, including metal oxides as well as elements like silicon and germanium. In insulators, essentially all the electrons are tightly bound to atoms or ions, and none are free to move under an external electric field. In effect, these materials do not conduct electricity at all. In metallic conductors, essentially all the atoms are ionised, providing free electrons, which move freely through the ions and can move under an external electric field.

    • Word count: 2379
  4. To build and calibrate a sensor in order to calculate the temperature of surroundings.

    SAFETY ASPECTS The main safety aspect to consider whilst doing this experiment involved the use of ethanol in the experiment, especially as I planned to heat it. As ethanol is flammable, I could not heat it with a naked flame, due to obvious fire risks. So instead I chose to use a water bath, using water I had heated to heat up the ethanol without the use of a flame. This lead to another risk, as electricity and water were both present in my experiment.

    • Word count: 2305
  5. Is a filament lamp an ohmic resistor?

    (ohms, ) Current (amperes, A) The filament of a bulb becomes hot because it resists the current flowing through it." Physics for today and tomorrow, 2nd edition: tom Duncan. Ohm's law: "When the same p.d. is applied across different conductors different current flow depending on how easily electrons can more in them. The opposition of a conductor's to current flow is called its resistance. A long thin wire has more resistance than a short thick one of the same material because a given p.d. causes a smaller current in it." "A good conductor has a low resistance and a poor conductor as a high resistance.

    • Word count: 2234
  6. An Investigation into the Resistance of a Thermistor, its Application as a Sensor and Within a Potential Divider

    However as mentioned above, the resistance change is non-linear which is a drawback as it means that calibration is required. Standard thermistors operate from -55 �C to 150 �C although some have been shown to operate up to 300 �C. I have decided to use a thermistor in this investigation due to its stability, resolution/sensitivity, suitable range, consistency and low cost. As a medium in which to test the thermistor's behaviour, I have chosen distilled water - It is accessible, has a low viscosity, and a high specific heat capacity.

    • Word count: 2879
  7. Investigating the Resistance Of A Light Bulb As The Voltage Is Increased.

    For this experiment I will be using a series circuit rather than a parallel circuit. This is because I only need to test the resistance of one light bulb rather than testing three or four light bulbs in a parallel circuit. This way the lamp will be more efficient. Safety To make sure that the test is safe, I would make sure that I would be working away from any water sources, because water is a conductor which could cause shorting and electric shocks. I would also check if any wires were frayed because if I touched one again I could get an electric shock.

    • Word count: 2146
  8. The electrolysis of copper from copper sulphate solution

    I could carry out the experiment in two ways; the first would be to measure the change of mass of the copper. However, this method is very difficult to carry out, the reason for this is, you need to take into account the original mass of the electrodes, and you need to be very accurate on knowing if ALL of the copper has been taken from the electrodes, the reason being because some of it could still be left behind and may be very hard to pick up and see. The second and easier way, is to measure the current.

    • Word count: 2084
  9. Find out which circuit is suitable for a range of resistances that an ammeter and voltmeter can measure.

    In circuit 2, the voltmeter is connected in parallel across the resistor and the ammeter. This may affect the resistance value recorded. I need to work out the value of the resistors that I will use, to do this I will have to consider the accuracy of the ammeter and the voltmeter. From the manufacturers specifications printed on the ammeter and the voltmeter, I know that the ammeter can measure a maximum of 2 milliamps and has a resistance of 40 ohms.

    • Word count: 2469
  10. Magnetism Investigation

    sqrt(epsilon * mu) where epsilon is the permeability of free space. If a long, straight conductor carrying current I' is placed in a magnetic field of strength B, the conductor will experience a force whose magnitude on a length L of the conductor is given by F = I' * L * B * sin(theta) (3) where theta is the angle between the current and field directions. The force F has the units of newtons if B is measured in teslas, I' in amperes, and L in meters. Now, if two long, parallel conductors carrying currents I and I' are separated by a distance d, each will experience a force due to the magnetic field set up by the other.

    • Word count: 2277
  11. Investigating The Resistance Of A Light Bulb As The Voltage Is Increased.

    To make the test safe I would make sure that I would work away from water, make sure my hands were dry and not sweaty as water is a conductor which could cause shorting and electric shocks. I would also check if any wires were frayed because if I touched one again I could get an electric shock. I would also check if the cable to the plug connecter was properly connected to the plug grip as loose wires in the actual plug could cause shorting and possibly a fire.

    • Word count: 2419
  12. An investigation into how the strength of an electromagnet is affected by varying the current

    To become magnetic in the first place, the electrons in the c-core (the one with the wires around) will have to align themselves. This happens when they group together in domains. The majority of these domains are usually only partly aligned. When every electron in every domain is aligned, then the magnet has reached its potential and is described as "saturated." I also know that if there are more coils around the core, the electromagnet is stronger. Also the type of wire Will affect the electromagnet's strength. I will use the Internet or an encyclopaedia to help me.

    • Word count: 2148
  13. Diode Application in Rectifier Circuits

    The AC on each side of the center-tap is ½ of the total secondary voltage. Only one diode will be biased on at a time the prose to be center tap full-wave rectifier is like below. Last is about full-wave bridge rectifier circuit, The Bridge is shown in the figure below. The circuit has four diodes connected to form a bridge. The ac input voltage is applied to the diagonally opposite ends of the bridge. The load resistance is connected between the other two ends of the bridge.

    • Word count: 2206
  14. Geothermal energy is not easily accessible with our current technology. Our main focus was to figure out methods of harnessing this energy with new innovations based off of current technologies

    Each of these processes has its own set of limitations. Basaltic magma is the most common type of magma and it has a low viscosity, which means it is able to flow freely. This low viscosity allows dissolved gasses to escape which prevents gas pressure from accumulating in magma chambers. Because of this, basaltic magma would be the most logical to generate and utilize. Raising the geothermal gradient would increase the formation of magma. As mentioned before, it could be created by radioactive heat, frictional heat, and decompression due to convection.

    • Word count: 2464

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