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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

    Internal Resistance of a cell

    5 star(s)

    through that circuit defines quantitatively the amount of electrical resistance R. Precisely, R = V/I. Thus, if a 12-volt battery steadily drives a 2-ampere current through a length of wire, the wire has a resistance of 6 volts per ampere, or 6 ohms. Ohm is the common unit of electrical resistance, equivalent to one volt per ampere and represented by the capital Greek letter omega, ?. The resistance of a wire is directly proportional to its length and inversely proportional to its cross-sectional area. Resistance also depends on the material of the conductor.

    • Word count: 2385
  2. 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
  3. Marked by a teacher

    viscosity of golden syrup

    4 star(s)

    multiplying it by gravity and then the density of steel to calculate the weight of the ball bearing and calculate the downward force on the object. This came about as m=?V and W=mg. Substituting in W= ?Vg. The volume of a sphere = 4/3?r3. Substituting in again, W=4/3?r3?steelg. r= radius of sphere (m) ?steel=density of steel (7.8 g/cm3) g=gravity (9.81m/s2) However, there is more than this acting on the ball bearing. Viscous drag is a force opposing the weight of the object and this is calculated by using Stokes' law.

    • Word count: 3734
  4. 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
  5. Marked by a teacher

    Experiment to find the specific heat capacity of an aluminium block.

    4 star(s)

    Where Q= energy transfer C= specific heat capacity We can rearrange this to give: C= Q/(m(T2-T1)) And as power = energy/time Therefore E= Pt = Q And P = IV therefore Q = IVt Hence C= IVt/(m(T2-T1)) Which is rearranged to the form y=px + c to give: T2= (IVt / (m.C)) + T1. Where p is the gradient, and equals 1/C, therefore x = IVt/m = Q/m, and y = T2 the y intercept is equal to T1 Therefore I have calculated this table: Energy transfer Errors (J)

    • Word count: 616
  6. 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
  7. Peer reviewed

    Measurement of the resistivity of Nichrome

    5 star(s)

    material (measured in ohms, ?); > L is the length of the piece of material (measured in metres, m); > A is the cross-sectional area of the specimen (measured in square metres, m�). From this equation, I can see that the resistivity will be the resistance over length multiplied by the cross-sectional area. I rearranged the equation and substituted into the straight line equation as is shown below. y = mx + c R = ?L /A R?L The value of resistance of the material is depends on the value of the length.

    • Word count: 2614
  8. 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
  9. 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
  10. 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
  11. 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
  12. Peer reviewed

    Electrical Hazards.

    4 star(s)

    The conductivity is usually small, but can be increased if the body or clothing is wet. The risk of injury also increases according to the size of the voltage or current, or the duration of contact. There is a risk of electrocution (death by electric shock) if current passes across the heart. For example, if one foot is touching wet ground, the risk is greater if the arm on the opposite side touches a high-voltage source than it would be if the arm on the same side did so. Current passing into the body generates heat, which burns the tissue.

    • Word count: 738
  13. 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
  14. Peer reviewed

    To determine the internal resistance of a dry cell using an ammeter and a voltmeter.

    3 star(s)

    However ,if the cell is connected across an external resistor as shown amount of energy per unit charge is wasted in getting through the cell. V = ? - Ir Therefore ,V is less than ?,then not all the energy per unit charge supplied by the cell is transformed in the external circuit into other forms of energy . It implies that a certain amount of energy per unit charge is wasted in getting through the cell. The internal resistor of a cell depends on several factors and is seldom constant .

    • Word count: 844
  15. 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
  16. Physics - How Electric Eels Generate and Use Electricity.

    Unspeakably even their intestines are shortened and looped making it more closer to the front of the body. Electric eels tend to live in murky, muddy waters and usually live with poor eyesight. They are most known to be found in the ponds of the Amazon and also Orinoco basins of South America. One very thrilling fact about these eels is that they use a low voltage charge to sense their whole surroundings and to navigate and swim through the water. If threatened by any other animals they use their bodies which contain 6,000 specialized cells names electrocytes that are basically cells that store power just like batteries.

    • Word count: 1820
  17. How does physics affect chocolate making?

    If it is a liquid the viscosity will increase, if you decrease the temperature. However in a gas, the viscosity will increase if you increase the temperature. In the production of chocolate the temperature must be average, so that it flows quickly while producing, but must be viscous enough to be moulded to the desired shape. Also the cross sectional area affects the stress required to break it, this will in turn affect the texture.

    • Word count: 475
  18. Photovoltaic cells case study

    A certain portion of the photons from the light that strikes the cell is absorbed and then transferred into the semiconductor material. The electrons then flow freely (DC current), having the energy being shifted in to them.[3] The current produced is directly dependent on the amount of light that reaches the cell. Therefore; the more light energy, the more current and potential difference, and therefore more power. P = I x V The energy given to excite the electrons away has to be greater than the energy given to the electrons if they excite and then relax to return to

    • Word count: 591
  19. Investigate how the charge on a capacitor is related to the potential difference applied across it by charging the capacitor at a constant rate.

    Then, . If a capacitor is charged up at a constant rate, i.e.=I, where I is a constant. Then= is also a constant. Hence, the potential difference across the capacitor increases linearly with time. Data Analysis: The result of this experiment is shown as below: p.d. across capacitor V 1V 2V 3V 4V 5V 1st attempt Time t 5.92s 11.73s 17.67s 23.67s 29.42s 2nd attempt Time t 5.90s 11.30s 16.87s 22.71s 28.59s 3rd attempt Time t 5.19s 10.75s 16.94s 22.85s 28.72s Discussion: When the capacitor is being charged up, the microammeter reading decrease with time, and the CRO trace reading increase constantly.

    • Word count: 479
  20. Free essay

    Measurement of capacitance by reed switch.

    The charge on the capacitor is : When the switch is in contact with C, the capacitor discharges through the micro ammeter. This process of charging and discharging occurs times per second. In each second, pulses of charge () flow through the micro ammeter. Hence, the current () through the micro ammeter is given by : Procedures 1. The circuit was connected as shown in the setup of the diagram. The resistance of the variable resistor was set at its maximum value.

    • Word count: 965
  21. 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
  22. Investigation On The Resistivity Of Apples. Since we are measuring the resistance of an apple, when the length increases, resistance will increase. Although we are mostly measuring the water content in the apple, we are also measuring the resistance of th

    The only thing is to be careful with the knife and do not play with it or swing it around. Preliminary method 1. Using the ruler and pencil, mark the places of the apple to cut. 2. Cut three 1 x 1 x 1 cm slices of apple with the fruit knife. 3. Repeat step 2, with 2 x 1 x 1 cm, 3 x 1 x 1 cm, 4 x 1 x 1 cm, and 5 x 1 x 1 cm slices of apple.

    • Word count: 2042
  23. 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
  24. 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
  25. Magnetic fields around electric currents

    The horizontal component of the magnetic field will be measured. This is not the maximum magnetic field that we want. 8 Why the sensitivity of the search coil can be increased by increasing the frequency? The more frequent the voltage across the wire, the more frequent is the change of the magnetic field. The magnetic field across the search coil is proportional to the sensitivity. 9 Tabulate the length l of vertical trace on CRO and current I measured in the table below: Length of vertical trace on CRO l/cm 1.2 2 3.4 4.6 6.2 7.6 8 Current I/A 0.1 0.2 0.3 0.4 0.5 0.6 0.7 10 Plot a graph of l against I.

    • Word count: 561

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