A resistor's resistance is found from Ohm's law,

PHYSICS · Subjective · Fermi University Physics · Scientific Practice & Experimental Methods · Uncertainty in measurement · Uncertainty in measurement

Measurement and Method, Ch Type A, Type B and the uncertainty budget

Problem

R = V/I

. The ammeter used is believed to have a small zero-offset

\delta_{\rm off}

on its current reading, with best estimate zero, so the measurement model is

R = V/(I-\delta_{\rm off})

. Eight independent voltmeter readings across the resistor give a mean

\bar V = 5.000\,\mathrm{V}

with sample standard deviation

s = 0.006\,\mathrm{V}

. The voltmeter's calibration certificate states the reading is correct to within

\pm 0.5\,\%

of reading at coverage factor

k=2

. The ammeter reads

I = 0.2000\,\mathrm{A}

(a single reading, judged stable) with display resolution

0.0001\,\mathrm{A}

. The zero-offset

\delta_{\rm off}

is judged, from repeated checks with the circuit open, to lie within

\pm 0.0002\,\mathrm{A}

of zero, with nothing favouring any part of that range. (a) Evaluate the standard uncertainty of each row (state the type and distribution assumed for each). (b) Combine the two voltage rows into

u(V)

and the two current rows into

u(I)

. (c) Propagate to

u_{\rm c}(R)

and quote

R

with its standard uncertainty. (d) Identify the dominant row and say what should be improved first.

Browse the problem library