MP0ManualApp - MP0 Propagation of Errors PHY 257 I...

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1 MP0 Propagation of Errors PHY 257 I. Objective. To study the propagation of errors II. Equipment: Incandescent light source, component carriers, optical bench, lens (f = 127 mm), screen. III. Introduction. In many experiments we wish to determine the quantity z which is connected with a parameter x through the equation: ) ( x f z = . First we measure x with an uncertainty σ x and using the expression ) ( x f z = we then determine z . For example, the area A of a square of side a is given by the equation: 2 a A = . The uncertainty σ x in the parameter x will propagate through the function f and result in an uncertainty σ z in the parameter z . The general expression for σ z is given by the equation: x z x f σ σ = In a different type of experiments the parameter z we wish to determine depends on two other parameters x and y through the equation: ) , ( y x f z = For example in order to determine the resistance R of a resistor we measure the voltage V applied across the resistor and the current I that passes through it. The resistance R is given by the equation: I V R = . In the course of such an experiment we measure the parameters x and y with uncertainties σ x and σ y , respectively. These uncertainties propagate through the function f and result in an uncertainty σ z of the parameter z .
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