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152-ECO Manual Addendum Rev 2

152-ECO Manual Addendum Rev 2 - EC0 Propagation of Errors...

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1 EC0 Propagation of Errors. PHY 152 I. Objective. To study the propagation of errors II. Equipment: Analog ammeter, digital voltmeter, switch, resistance box, DC power supply, unknown resistors 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 . Below we give the resulting uncertainty z z in some frequently encountered cases: m x z , x m z x z eq.1 x e z , x z z eq.2 ) ln( x z , ) ln( x x z x z eq.3 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
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