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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. How the resistance of an ammeter changed when introduced into a circuit.

    To take the voltage of an object, the shunting resistor must be placed in series, as the resistance of the moving-coil galvanometer is not very high. Some formulae which may be useful during this experiment is: Method The experiment firstly started by looking at calculating the resistance of the voltmeter. This was done by setting the circuit up as below: E = d.c. power supply M = Voltmeter being tested Rm = Voltmeter resistance I = Current The avometer was then placed upon successive ranges of 3v, 10v, 30v, followed by the digital voltmeter on ranges 1v and 10v.

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  2. Aim: To find out the internal resistance and EMF of a given power supply.

    I (Current) V (Volts) 1 1 0.47 2.2 0.35 0.72 3.9 0.2 0.87 4.7 0.15 0.94 10 0.1 1.08 15 0 1.15 22 0 1.18 33 0 1.21 47 0 1.23 100 0 1.26 150 0 1.27 Duracell Procell Size D 1.5V R (Ohms) I (Current) V (Volts) 1 0.55 0.41 2.2 0.38 0.8 3.9 0.24 0.95 4.7 0.2 0.97 10 0.1 1.1 15 0.09 1.15 22 0.08 1.8 33 0.03 1.2 47 0.02 1.22 100 0.01 1.24 150 0 1.26 Mains Power Supply R (Ohms)

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  3. Aim: To investigate the factors affecting the e.m.f. induced in a coil due to a varying magnetic field in a neighboring coil.

    = -NAdB/dt Procedures: A. Rate of change of magnetic flux 1. A square solenoid was connected to a signal generator through an a.c. ammeter. 2. 10 turns of a copper wire were winded tightly around the middle of the solenoid and the wire was connected to a CRO. 3. The signal generator was turned on and set to 1 kHz. The CRO setting was adjusted to display a whole trace on its screen. 4. The time base of the CRO was switched off.

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  4. A superconductor is a substance which conducts an electric current with zero resistance. It also repels magnetic fields perfectly at a certain point which is also known as the Meissner effect.

    They discovered it by examining the magnetic properties of materials as they became superconductive. The Meissner effect is now used as a routine test for superconductivity. During 1941 -1953, niobium-nitride and vanadum-silicon were found to superconduct at 16 degrees Kelvin and 17.5 degrees Kelvin respectively. In 1962, scientists at Westinghouse developed the first commercial superconducting wire with an alloy of niobium and titanum (NbTi). The first widely accepted theoretical explanation of superconductivity, now known as the BCS theory, was created in 1957 by American physicists John Bardeen, Leon Cooper, and John Schrieffer. They then won a Nobel prize in 1972.

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  5. Superconductivity. 907349

    In a superconductor, the resistance drops exactly to zero when the material is cooled below its critical temperature (the temperature at which electrical resistance is zero). So an electrical current flowing in a superconducting wire can persevere with NO power source. In superconductivity materials, its characteristics appear after it's cooled below the critical temperature (varies between materials).This is mostly between 20Kelvin to 1K, e.g. solid mercury has critical temperature of 4.2K. Metals undergo metallic bonding where they have delocalised electrons allowing them to conduct in the form of heat and electricity.

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  6. To investigate the capacitance and uncertainty of a capacitor.

    to reach particular values is recorded. * The experiment is repeated two more times so as to acquire three sets of time (T1, T2, T3) for the current (I) in question and the average time (t) was also recorded. * Using the average time a graph of lnI against t is plotted using the following equation: Where y= lnI, x= t, gradient = and lastly y- intercept = lnImax * Resistance(R) of uncertainty ?2% is measured using the multi-meter and the Capacitance (C) is found by using the gradient = ? Diagrams: Showing setup of circuits in question. Results: I(?A)

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  7. To investigate the relationship between the power consumed by a torch bulb and the resistance, by measuring the potential difference across the bulb and its current.

    The voltmeter is set to read volts and ammeter to read micro-amps. * The variable resistor (Rheostat) is adjusted until the current (I) observed on the ammeter is at its minimum value. * Readings are taken from each multi-meter. The ammeter gives the current (I) whilst the voltmeter gives the p.d across the bulb in question. * The variable resistor is adjusted so that the current (I) increases while the resistance (R) decreases. The readings of twelve (12) other points of equally spaced intervals are then taken so as to have thirteen (13)

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  8. Resistivity of Lightbulbs

    Increasing light levels increases output voltage and this is the light sensor. The Diagram below shows this: Choosing the correct Fixed Resistor: It is very important to ensure the correct Fixed Resistor is installed in the circuit. This is due to the ratio between the fixed resistor and the variable resistor, the LDR, needing to be as wide as possible thus giving an accurate sensor reading across the input range that it will be sensing. It is therefore necessary to trial various resistors and pick the resistance which results in the highest potential difference change across the fixed resistor for the sensing spectrum.

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  9. Coulombs Lab Report

    1 / r2 Substituting F for d, d ? 1 / r2 To turn that into an equation and not proportionality, we must insert some sort of constant, d = k / r2 This makes sense. If the objects have a greater charge, and thus have a great excess or deficit of electrons, they will have a stronger force of attraction or repulsion with the other object. Similarly, the closer the objects are together, the more unstable the electrons become and thus tend to increase the stronger force of attraction or repulsion between the objects.

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  10. Free essay


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  11. The aim of the experiment is to verify the maximum power theorem and investigate the efficiency with which energy is transferred from a source of e.m.f to a load resistance.

    In the above cases, we know that friction can be mainly divided into two types, which are static friction and kinetic friction. Static friction occurs when two surfaces are in contact but without any relative motion. It always acts in a direction along the surface and tends to oppose the relative motion. The magnitude of static friction increases with the applied force to oppose the star of motion, until reaches a certain value called limiting friction. Therefore, the applied force must be same as or larger than the limiting friction in order to make the object to move.

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  12. In this experiment, we will measure the e.m.f. and the internal resistance of a dry cell.

    Simply, A Voltage where the charge is gaining energy is an electromotive force. It is total opposite the potential difference (p.d), which is the energy released when a unit of charge passes between two points. Dry cell is very common in daily life and has a wide variety of usages. In an ideal dry cell, there should be no any resistance. However, in the reality, there is no ideal dry cell and it must have an internal resistance. Internal resistance of a dry cell just like that there is a resistor in the dry cell.

    • Word count: 2557
  13. Sensors Project Report

    It is not very accurate because the thickness of paper varies from one side of the paper to another and from one piece of paper to the other. - Using a log Potentiometer to determine the number of sheets of paper in the sensor by the thickness of the paper (number of papers) and that varies the ratio of the resistance in the potentiometer so the number of papers can be determined by the ratio. From all the choices above, the potentiometer is chosen because it is more related to the work in the syllabus and it is one of the most accurate ways to measure among the others that have been suggested.

    • Word count: 2031
  14. Studying a simple harmonic motion

    Two widely spaced dots on the tape were marked- this gave the zero position of the pendulum bob. (4) On the tape every 3rd dot from the zero position was marked off. The displacement of these points from the zero position was measure and the corresponding time was worked out. Time interval between successive dots = 3(1/50) =0.06s (5) The data for time and displacement were entered in columns A and B respectively in a spreadsheet program. The following formulae were entered in the cells flagged: C2= (A2 + A3)/2 the mid-point between times A2 and A3 was found; D2= (B2 +B3)/0.06 the average velocity between displacement B2 and B3 was found; E3= (C2 + C3)/2 the mid-point between times C2 and C3 was found; F3= (A2 + A3)/0.06 the average acceleration between velocities D2 and D3 was found.

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  15. Investigating electric potential between two parallel plates and around a charged sphere using a flame probe

    Potential between two parallel plates (4) The apparatus was set up as above. The metal plates were placed 0.15 m apart. The EHT supply was adjusted to 1.5 kV. Make sure that the wire which connected the probe and the electroscope did not touch the bench or any earthed conductor. (5) The flame probe was lighted. It was moved across the earthed plate to the positive plate and the deflection of the leaf was observed. (6) The flame probe was moved in a plane parallel to the metal plates. The deflection of the leaf was observed (7)

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  16. Charging a capacitor at a constant rate

    (2) The time base was set to any high value so that a steady horizontal trace is displaced. The trace was set to the bottom of the screen. (3) The capacitor was shorted out by connecting a lead across it and the 100k? potentiometer was adjusted for a suitable current, say, 80�A. (4) The shorting lead was removed and the capacitor would up charged up. Note what happened to the microammeter reading and the CRO trace. (5) The procedure was repeated but this time the stop-watch was started and the potentiometer was adjusted continuously to keep the current constant as the capacitor charged up.

    • Word count: 566
  17. Is polymer electronics the future of TV screens

    Each pixel is then lit up in slightly different colours to create a picture. This technology is now starting to become obsolete, as the public are wanting thinner more efficient TVs, that don't have to be the centre piece of a room, but placed on a wall like a picture, and go reasonable unnoticed. People are also seeking a better quality picture, which is like real life. The picture quality of TVs has change hugely since the CRT screens, but people still demand a better picture. The most recent advance in TV screens is the development of polymer electronics, producing TV screens known as OLEDs.

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  18. Light notes

    The colours of the complete spectrum are red, orange, yellow, green, blue, indigo and violet. The atoms in an object control which frequencies are absorbed and which are reflected. There is no colour in objects. Which frequencies of light are reflected by an object controls what colour you see. The colour of a filter depends on which of the frequencies it allows to pass through. We call it red light but it is just the light with the frequency that causes the brain to make you think the object is red. The primary parts of the complete spectrum are red, green and blue.

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  19. Light intensity notes

    This gives a baseline of 2Au = 300 Million km. The angle subtended by the distant star and the two viewing points in two lots of the parallax angle. So using the diagram parallax angle = . This method is only really usable over relatively short distances. The Parsec A parsec, or 1 pc, is a unit of distance. It is defined as the distance between the Sun and an object when the parallax angle is equal to one second of arc ( of a degree). The 1 Au on the diagram is the distance between the Earth and the Sun.

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  20. Light and matter notes

    - the diffraction of light when it passes the edge of an object or passes through an opening. Wave Model for Light The Wave Model of light compares light to a smooth and continuous train of transverse waves. The Wave Model successfully predicts light will: - travel in straight lines at constant speed. - reflect of surfaces with the angle of incidence equal to the angle of reflection. - have an intensity that follows and inverse square law with distance.

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  21. Plotting the decay curve of charge in a capacitor

    Measurement of charge by an electrometer 1. The circuit as shown in Fig.1 was connected to calibrate an electrometer. 2. The potentiometer was adjusted to apply 1V to the input sockets of the electrometer. The milliammeter should give a full-scale deflection, which means that the reading of the milliammeter having a full-scale deflection represents 1V. If not, the internal pre-set control of the electrometer should be adjusted or the other one can be used. The potentiometer was disconnected from the electrometer.

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  22. Investigation of factors affecting the capacitance of a parallel plate capacitor using electrometer

    Tabulate the results. Voltage (V) / V 5 10 15 20 25 30 35 Charge (Q) / ? 10?8 C 0.19 0.36 0.50 0.70 0.93 1.05 1.24 10. Plot a graph of the charge stored (Q) in the parallel plate capacitor against the potential difference (V) across it. B. Factors affecting the capacitance 12. Repeat steps 6 to 8 with different numbers of spacers (n) between the metal plates. Tabulate the results. Find the reciprocal of the number of spacers (1/n). No. of spacers (n) 1 2 3 4 5 6 7 1/n 1.00 0.50 0.33 0.25 0.20 0.17 0.14 Charge (Q)

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  23. Measurement of capacitance by reed switch

    Repeat steps 3 and 4 with the other frequencies of the signal generator from 400 Hz to 10 Hz. Tabulate the results. Frequency (f) / Hz 100 150 200 250 300 350 Current (I) / ?A 1200 2000 2500 3200 3600 4300 Note that low switching frequency is advised since for high one, the reed switch may not be sensitive enough to respond, and the time may be too short for complete discharge. 6. Plot a graph of frequency (f) against current (I). Results and Discussion 1.

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  24. Objective To investigate the relationship between the charge on a capacitor and the p.d. across the capacitor by charging at a constant rate.

    > Clip component holder > Hand-held stop watch > CRO > Connecting leads Procedure 1. Connect the following circuit. Set the CRO to d.c. and the sensitivity to 1 Vcm-1 2. Set the time base of the CRO to a high sweep rate so that a steady horizontal trace is displayed. Shift the trace to the bottom of the screen. 3. Short out the capacitor by connecting a connecting wire across it (XY). Adjust the 100 k? potentiometer to a suitable value for a steady current to flow (e.g. 80�A). 4.

    • Word count: 463

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