A resistance is found from Ohm's law

PHYSICS · Multi-part · Fermi University Physics · Scientific Practice & Experimental Methods · Mathematical Methods for Physics · Uncertainty in measurement

Mathematical Methods for Physics, Ch Partial differentiation, chain rules and Jacobians

Problem

R = V/I

, using a voltmeter reading

V = 12.0 \pm 0.1\,\mathrm{V}

and an ammeter reading

I = 0.400 \pm 0.005\,\mathrm{A}

, the two uncertainties being independent and random, each as likely to fall one way as the other. A technician writes: "the fractional uncertainty in a quotient is the sum of the fractional uncertainties, so

\delta R/R = \delta V/V + \delta I/I

, and this gives the uncertainty in

R

." ((a)) Compute

R

and the technician's value of

\delta R

. ((b)) Give the correct value of

\delta R

from the rule for combining independent uncertainties, and state by how much the technician's figure overestimates it.

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