OCR A-Level Physics

Designing an investigation

An experiment tests how one quantity depends on another, so the first job is to decide which quantity you will change and which you will measure. The independent variable is the one you change deliberately, and the dependent variable is the one you measure as a result. Every other quantity that could affect the result is a control variable and has to be kept constant, because otherwise a change in the dependent variable could be caused by something other than the one you meant to alter.

A plan should say how each variable will be measured, with which instrument and to what resolution, and how each control variable will be held steady. In a test of how the resistance of a wire depends on its length, for example, the length is the independent variable and the resistance the dependent variable. The controls are the wire's material, its diameter and its temperature. Temperature is the awkward one, because the current heats the wire, so the plan should use a low current and switch it off between readings.

The instrument must have a resolution that suits the size of the quantity. A metre rule with 1 mm divisions is fine for a length of 80 cm, where a reading is uncertain by about 1 part in 400, but it is poor for a wire of diameter 0.5 mm, where the same uncertainty is larger than the thing being measured. That is why a micrometer is used for the diameter. Choosing apparatus therefore means estimating the size of each quantity first, then picking an instrument whose smallest division is a small fraction of that size.

A good plan also covers:

• the range of the independent variable, with enough values (usually at least five or six, evenly spread) to show a pattern;
• repeat readings at each value, so that a mean can be taken and an anomalous result noticed;
• a way of reducing the main sources of uncertainty, such as timing many oscillations instead of one;
• the safety measures needed, with the hazard named and the step that reduces the risk;
• a description of how the data will be analysed, including which graph will be plotted and what its gradient or intercept will give.

The last point is where most plans are weak. If the aim is to find a constant, the plan should rearrange the equation into the form $y = mx + c$ before any measurements are made, so that it is clear what to plot.

Reading instruments

Analogue instruments

With a scale such as a ruler, a thermometer, a pressure gauge or a protractor, the reading is taken to the nearest division or, by interpolation, to a fraction of one. The eye must be level with the scale, because reading from an angle gives a parallax error. A zero error arises when the instrument does not read zero when it should, and it is corrected by subtracting it from every reading.

Vernier callipers

A vernier scale slides along a main scale and lets a length be read to a tenth of the smallest main-scale division. The main-scale reading is taken at the zero of the vernier scale, and the extra fraction comes from the vernier line that lines up exactly with any main-scale line. On common callipers the main scale is in millimetres and the vernier reads to 0.1 mm or 0.05 mm, and digital versions read to 0.01 mm. The callipers are closed first to check for a zero error.

Micrometer screw gauge

A micrometer measures small lengths such as the diameter of a wire, typically to 0.01 mm. The reading is the whole and half millimetres visible on the sleeve plus the hundredths shown on the thimble. With the sleeve showing 4.5 mm and the thimble line at 27 on the scale, the reading is $4.5 + 0.27 = 4.77\,\mathrm{mm}$. The ratchet is turned to close the jaws because it slips at a fixed force, which stops the wire being squashed and the gauge being over-tightened. The diameter of a wire is measured at several positions and in two perpendicular directions, since a wire is rarely perfectly uniform, and the mean is used.

Digital meters and timers

A multimeter measures current, potential difference and resistance on the range chosen. An ammeter is connected in series with the component, so that the same current passes through both, and a voltmeter is connected in parallel across it, so that it shares the potential difference. A digital reading has a resolution of its last digit, and the choice of range changes it, so the smallest range that does not overload the meter is used.

A stopwatch is limited not by its display but by the reaction time of the person using it, about 0.2 s, which dominates the uncertainty for any short interval. Light gates connected to a timer remove that problem because the beam itself starts and stops the clock, and they measure intervals of a millisecond or less. They are used for the speed of a trolley or a falling object, where a stopwatch would be inadequate.

Methods that improve accuracy

Some measurements can be made more precisely by changing the method rather than the instrument:

• timing a large number of oscillations, then dividing, so that a fixed reaction-time error becomes a small fraction of the total;
• using a fiducial marker, a small pointer or mark placed at the equilibrium position of an oscillator, so that the start and end of each swing is judged against a fixed reference;
• using a set square or a plumb line to make sure a length is measured at right angles to a surface or truly vertically;
• measuring a long distance in one go rather than adding many short ones, and measuring several wire turns or several wavelengths together and dividing.

The oscilloscope and signal generator

A signal generator supplies an alternating potential difference of chosen frequency and amplitude. An oscilloscope displays how a potential difference varies with time as a trace, with time along the horizontal axis and potential difference up the vertical axis. Two controls set the scales. The time-base sets the time represented by each horizontal division, in s/div or ms/div, and the volts per division setting gives the potential difference represented by each vertical division.

The period is found by measuring the horizontal length of one complete cycle in divisions and multiplying by the time-base setting, and the frequency is the reciprocal of that.

If one cycle spans 4.0 divisions with the time-base at 5 ms/div, then

The peak-to-peak height is found in the same way. If the trace covers 3.0 divisions from its lowest to its highest point with the setting at 2 V/div, the peak-to-peak value is 6.0 V and the amplitude is 3.0 V. The frequency of a sound can be found by connecting a microphone to the oscilloscope and reading the period off the trace, and an oscilloscope can also show the time between a pulse leaving a transmitter and arriving at a receiver.

Building and checking circuits

A circuit is built from a circuit diagram by starting at one terminal of the supply and following a single loop through the series components, and then adding the voltmeters across the components they measure. Polarity matters for some components, including diodes, LEDs, electrolytic capacitors and meters, and these have to be connected the right way round. Before switching on, the circuit is compared with the diagram, and a variable resistor or a potential divider is set so that the current starts at its smallest value.

Faults are traced by checking that a component which should have a potential difference across it does, and that a break in the circuit shows up as the full supply voltage across the gap. Switching a current off between readings stops wires and filaments heating up, which would change their resistance and so invalidate the results.

Waves, light and radiation

Waves can be generated in several ways, depending on what is to be shown. A ripple tank shows reflection, refraction and diffraction of water waves, with a strobe light or a camera used to freeze the pattern. A loudspeaker driven by a signal generator produces sound of a known frequency, and a microphone with an oscilloscope detects it. A vibration transducer drives a stretched string, and a microwave or radio transmitter and receiver show polarisation and interference of electromagnetic waves.

A laser is used to investigate interference and diffraction of light. The beam must never be directed at anyone's eye, nor allowed to reflect from shiny surfaces into one, and the laser is chosen to be of a low power class.

Ionising radiation is investigated with a Geiger-Muller tube and counter, or a ratemeter. The background count is measured first with no source present, and subtracted from every reading. Sources are handled with tongs, kept in their lead-lined containers and kept as far from the body as practical, and the time they are out is kept short, because the dose falls with both distance and time.

Computers and sensors

Data loggers connected to sensors record quantities such as temperature, light intensity, sound level, force or position at a chosen rate, which suits fast changes such as a falling mass, a discharging capacitor or a cooling liquid. Software can then tabulate the results, plot graphs and find gradients, and a spreadsheet can also be used to model a process by repeating a simple calculation over many small steps. Computer modelling of this kind, for example of radioactive decay or capacitor discharge, is checked by comparing it with measured data.

Recording results

Results go into a table before any calculation is done. Each column heading gives the quantity and its unit, written with a solidus, such as $t\,/\,\mathrm{s}$ or $I\,/\,\mathrm{mA}$, and the numbers underneath carry no units of their own. Raw readings are recorded to the resolution of the instrument, the same number of decimal places in a column, and any repeats and their mean are shown. Calculated values, such as a mean or $1/I$, are given to no more significant figures than the least precise quantity used to find them.

Safety

A risk assessment names the actual hazard and says how the risk is reduced, rather than just saying "be careful". Examples include:

• hot water, wires and metal blocks, where the risk is reduced by using insulated handles or waiting for things to cool, and by keeping the water below boiling point where possible;
• mains-powered and high-voltage equipment, where the supply is checked and switched off before any change to the circuit;
• falling masses, where a tray of sand or a box is placed underneath and feet are kept clear;
• springs and wires under load, which can snap, so eye protection is worn and the load is kept below the breaking limit;
• lasers, as above, and radioactive sources, as above.

Techniques named in the course

The practical techniques the course expects are each covered with the topic they belong to. They include the motion of trolleys and collisions, the acceleration of free fall, terminal velocity, force-extension and the Young modulus, the characteristics of electrical components, the resistivity of a metal, the internal resistance of a cell, potential dividers, waves (oscilloscope frequency, ripple tank, polarisation, superposition, the wavelength of light with a double slit and a grating, the speed of sound by resonance, refraction and total internal reflection), the Planck constant with LEDs, specific heat capacity and specific latent heat, the gas laws and an estimate of absolute zero, circular motion with a whirling bung, simple harmonic oscillations, capacitors in series and parallel and their charge and discharge, the magnetic flux density between poles, magnetic flux with search coils, transformers, and the half-life of protactinium and the absorption of radiation.