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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.

  • Marked by Teachers essays 5
  • Peer Reviewed essays 9
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  1. Marked by a teacher

    Sensing project

    5 star(s)

    Alternatively a different sensing circuit could be used. A circuit with a thermistor (a component sensing change in temperature) could be used. In normal situations when the window would be fully closed the temperature in the greenhouse would be high so the output voltage from this circuit would be low. However if the windows were to slip open fully then the temperature inside the greenhouse would decrease so the output voltage would increase. The circuit could be linked to an alarm of some type so as when the voltage increases past a certain point when the window is fully open, the alarm rings alerting the gardener to shut the windows again.

    • Word count: 1875
  2. Marked by a teacher

    Determining Avogadro's Number Lab

    4 star(s)

    Uncertainty of moles Uncertainty of mass = Uncertainty of initial mass + Uncertainty of final mass Uncertainty of mass = 0.005 g + 0.005 g Uncertainty of mass = 0.01 g Percent uncertainty of mass = Percent uncertainty of mass = Percent uncertainty of mass � 1.89% The percent uncertainty for the number of moles is approximately 1.89%. Thus, the number of moles is approximately 0.00834 �1.89%. Current: Average charge = Average current x time After 10 minutes Average current = Average current = 0.9 A Percent uncertainty of average current = Percent uncertainty of average current � 11.1% The percent uncertainty for the average current is approximately 11.1%.

    • Word count: 1133
  3. I aim to find out how distance affects the light intensity emitted from an LED.

    These cells are used to generate environmentally friendly electricity for example a calculator that doesn't have batteries has one. I am going to use the LDR as it is easily available and has a reasonable degree of accuracy. As I said earlier the LDR is a resistor that changes resistance when the light intensity changes. So I could measure this with a multi meter set to ohms, or I could put it in a circuit with a ammeter as the current in the circuit will also change as the light intensity changes. It will change because the resistance will change.

    • Word count: 1739
  4. Peer reviewed

    Experiment: Decay of Charge in a Capacitor

    4 star(s)

    At any time, Or, , where I0 is the initial current through the resistor. Therefore theoretically, it is known that the decay of charge through constant resistance follows an exponential decay pattern. That is, the discharge rate is always proportional to the charge remained. The time constant reflects the time for the capacitor to discharge. The time required for the capacitor to discharge increases as the time constant increases. In an experiment, the time constant can be estimated by the equations above. Theories about Combination of Capacitors Consider the case when two capacitors are connected in series.

    • Word count: 1606
  5. Peer reviewed

    Investgating resistivity - Planning and Implementing

    4 star(s)

    Measure the diameter in three places, then compare these results. If they are not equal (to within experimental error) measure the wire's diameter more times, to ensure a reliable value for the diameter is found. Then the wire should be attached using sellotape to the metre rule so that it is taught and without kinks, to make measurements as accurate as possible. Set up the experiment as shown in the diagram. Attach one of the crocodile clips at the point marked 5cm by the rule (where its right-hand edge is at the 5cm line) and the other at the point marked 95cm (where its left-hand edge is at the 95cm line)

    • Word count: 1954
  6. Peer reviewed

    investigating the relationship between the diameter and the current in a wire at its melting point

    4 star(s)

    Aim of investigation The aim of this work is to investigate the relationship between the resistance and the diameter of the wire. Variables Variable Independent / Controlled / Dependent Resistance D Resistivity C Length of wire C Diameter I Prediction Since the theory suggests that So So the resistance should be inversely proportional to the square of the diameter of the wire. All of these values will be measurable or known, except for the resistivity, . Method Preliminary experiments Determining the size of the wire Use a micrometer to measure the thickness (diameter)

    • Word count: 1203
  7. Peer reviewed

    Power generation

    4 star(s)

    Another common method is to use combustion turbines to burn oil. In a fossil plant, oil, gas or coal is fired in the boiler, which means that the chemical energy of the fuel is converted into heat. Name of Fuel Calorific Value (J) Cost Coal 15-27 �3.10 per kWh Oil 15 �2.66 per litre Gas (natural) 13.9 �2.78 per litre Nuclear 38-90 �3.40 per litre Wind 47.3 �1.99 per litre Solar 141.7 �12.00 per kWh Geothermal 28-30 �3.05 per kWh Biomass 13 �1.68 per kWh Tidal 15-17 �3.60 per kWh Energy transfer diagram: Sun-->Light Energy-->Photosynthesis-->Plants/Animals-->Fossil Fuels The sun is the starting point for this energy chain, the source of the suns energy if nuclear fusion.

    • Word count: 1786
  8. Peer reviewed

    Solar cells

    3 star(s)

    a solar cell. By studying the relationship between external load on current and voltage, the internal resistance of a power supply can be determined. Knowledge gained can be used in designing a circuit that meets or exceed requirements that is required for a space exploration. Figure 1 Internal Resistance In a power supply there are wires and chemical electrolytes and electrodes that make up a cell which all have electrical resistance. Some energy produced by the power supply is transferred to the resistance.

    • Word count: 1379
  9. Peer reviewed

    Test of the reed switch capacitors in series and in parallel

    3 star(s)

    Assuming the capacitor is fully charged and discharged every time, the total charge Q total passing through the milliammeter per second is equal CVf, which is the theoretical current I. And the capacitance of the capacitor can be estimated by the formula C = I/ Vf. Capacitors in parallel If capacitors C1, C2, ..., CN are connected in parallel, the charges stored in each capacitor are shown as below: Q1 = C1V, Q2 =C2V, ..., QN =CNV, where V is the common p.d. across the capacitors. The total charge Q stored in the combination = Q1 + Q2 + ...

    • Word count: 1102
  10. Objective: To use a search coil and a CRO to investigate the magnetic fields generated by alternating currents through a straight wire and a slinky solenoid.

    produces a current which yields its own magnetic field. Its direction always opposes the flux change d?/dt. This fact is known as Lenz's law and is expressed by the negative sign. For a circular loop of radius r and area A = ? r2 in a constant magnetic field B (Fig. 36.2), the magnetic flux linkage ? is ? = B?A = BA cos? B? denotes the field component normal to the loop. The flux linkage is zero when loop and field are parallel. It is highest when the loop is perpendicular to the field, i.e. cos?=1, thus, ?

    • Word count: 1790
  11. Investigating the capacitance of a parallel report

    As Q= CV, with constant voltage supply, the number of charges stored is decreased. With the decrease of area of overlap, the capacitance is also decreased. Hence, the number of charges stored is also decreased. 3. Relative permittivity It is known that by putting a dielectric between the plates could increase the capacitance. A dielectric is a material that can be polarized by an electric field. When a dielectric material is placed in a uniform electric field, one surface will contain many positive ends of molecules and the other surface will contain many negative ends.

    • Word count: 1072
  12. P.d. of a supply delivering current

    across the terminals of a power supply as current is drawn from it. We shall see whether the p.d. is equal to the electromotive force(e.m.f) of the supply. Points about internal resistance we should know. i)The internal resistance of a power supply can be considered as a resistor connected in series with the power supply. ?)If there is a current flow, a voltage will be dropped across the internal resistance. ?)Terminal voltage = e.m.f of the power supply p.d. across point A is equal to p.d. across point B p.d. across point C is equal to p.d. across point D We can say that point A & B have same p.d.

    • Word count: 1145
  13. 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)

    • Word count: 1224
  14. 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.

    • Word count: 1401
  15. 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.

    • Word count: 1277
  16. 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)

    • Word count: 1441
  17. 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.

    • Word count: 1212
  18. 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.

    • Word count: 1230
  19. 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.

    • Word count: 1315
  20. 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
  21. 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
  22. 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
  23. 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
  24. 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

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