By B.A. Gregory
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Extra resources for An Introduction to Electrical Instrumentation and Measurement Systems: A guide to the use, selection, and limitations of electrical instruments and measurement systems
S. 414 respectively. Phase relationships When alternating signals are present in a circuit containing a combination of resistive and reactive (inductive or capacitive) components, a time displacement will exist between the signals at various points in the circuit. If the signals are all of one frequency this time displacement is referred to as a phase angle, but this latter term cannot be used if more than a single frequency is present. amplitude I I ,,,_... 28. 28 v = Vm sin () i = Vm sin (() + cp) Thus p = Vm sin () x 1m sin (() = Vm/ m sin () sin (() = Vm/m 2 + cp) + cp) [cos () - cos (2() - cp)] 46 AN INTRODUCTION TO ELECTRICAL INSTRUMENTATION Therefore the mean power over a cycle is the average power P = - 1 J211" -1 VrnIrn [cos cp - cos (2e - cp)] de 21T 0 2 I = -~ 41T 127T [cos cp - cos (2e - cp)] de 0 Examining the terms to be integrated, cos cp is a constant (cp does not change throughout a cycle), and cos (2e - cp) will go through two complete cycles as e goes from 0 to 21T, so its average value must be zero.
Ii) Detemination error This is the uncertainty in the indicated value due to the resolution of the instrument. the least decade of a bridge arm (or decade box) assuming that a detector of sufficient sensitivity is in use. (iii) Approximations of expressions In determining quantities by comparison methods the measurand is found by evaluating an expression. In deriving such expressions simplifications and approximations are often made. 3) which is Rx =~ + [m+:r+q (~ - ;)] In practice this equation is usually approximated to Rx = QS/M which is very much easier to handle but provides an answer that has an error due to neglecting the result of the terms in the outer brackets.
1). 6 INTERFERENCE Measurements involving small electrical signals can be seriously affected by the presence of interference, that is, the displayed quantity will be the sum of the desired signal and unwanted or interference signals. It is therefore necessary to ensure that instruments and connections are adequately protected from, and capable of rejecting, interference signals. 1 Environmental Interference The interference signals grouped under this heading are those related to effects dependent on such quantities as temperature, humidity, pressure, atmospheric pollutants, and so on.
An Introduction to Electrical Instrumentation and Measurement Systems: A guide to the use, selection, and limitations of electrical instruments and measurement systems by B.A. Gregory