Practical Skills and Experimental Methods
Measurement, uncertainty and graphs
Record measurements to the resolution of the instrument and include the unit. Uncertainty may be random or systematic. For repeated readings, uncertainty is often half the range or the standard deviation. Precision describes agreement between repeats; accuracy describes closeness to the true value. When adding or subtracting, add absolute uncertainties; when multiplying or dividing, add fractional uncertainties.
Experimental design and analysis
Identify the independent, dependent and control variables. Use appropriate instruments, repeat readings and plot a graph with labelled axes and units. Draw a line of best fit rather than joining every point. The gradient often gives the required quantity; the intercept may reveal a systematic effect. Error bars show uncertainty and can indicate whether a point is anomalous.
Worked example
A student measures V = 6.0 ± 0.1 V and I = 2.0 ± 0.05 A. R = V/I = 3.0 Ω. Fractional uncertainty in R = 0.1/6.0 + 0.05/2.0 = 0.0167 + 0.025 = 0.0417. Absolute uncertainty = 0.0417 × 3.0 = 0.125 Ω, which rounds to 0.1 Ω. The result is R = 3.0 ± 0.1 Ω. Quote the uncertainty to one significant figure and match the value’s decimal place.
Traps
Adding absolute uncertainties when multiplying or dividing; quoting too many significant figures; taking a gradient between two data points instead of using the line of best fit; ignoring zero error or parallax; failing to convert units before calculating; describing a precise set of readings as accurate without a true-value comparison.