A sensor's output voltage is read at four times after a switch is closed: : : with…

PHYSICS · Multi-part · Fermi University Physics · Scientific Practice & Experimental Methods · Data analysis and model fitting in the laboratory · Data analysis and model fitting in the laboratory

Measurement and Method, Ch Graphs, straight lines and least squares

Problem

A sensor's output voltage

V

is read at four times

t

after a switch is closed:

t/\mathrm{s}

0,\ 1,\ 2,\ 3

V/\mathrm{V}

10.0,\ 8.0,\ 6.1,\ 4.0

with standard uncertainties

u(V)/\mathrm{V} = 0.1,\ 0.1,\ 0.1,\ 1.0

(the last reading was disturbed by a brief mains interference and is known far less precisely than the others). Over this short interval

V

is expected to follow

V = c_0 + mt

. ((a)) State the weight

w_i = 1/u_i^2

of each of the four readings. ((b)) An unweighted fit, treating all four points as equally reliable, gives

m = -1.99\ \mathrm{V\,s^{-1}}

. Using the weights of part (a) in the normal equations' weighted form, calculate the weighted slope

m

. ((c)) State briefly why the weighted and unweighted slopes come out different, referring to which point's influence changed.

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