- L302-6.5 Drexel University Electrical and Computer Engineering Dept Electrical Engineering Laboratory II ECE L 302 C O Nwankpa Measuring AC

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L302-6.5 Drexel University Electrical and Computer Engineering Dept. Electrical Engineering Laboratory II, ECE L 302 C. O. Nwankpa Measuring AC Electric Power “This endless circulation of electric fluid may appear paradoxical, but it is no less true and real, and you may feel it with your own hands.” -Alessandro Volta Table of Contents Educational Objective Introduction Theory Steps Educational Objective The object of the experiment is to learn how to appreciate AC circuits by understanding the main components as well as variables that are influenced by them. These variables are AC voltages and currents. AC power will be shown to be the result of calculations involving these variables. Introduction In order to fully understand AC circuits, a popular tool will be reintroduced. This tool is referred to as phasor diagrams. Phasor diagrams describe time-varying quantities such as voltages and currents using complex number representation: V V θ = V I I = I In this course we shall appreciate the use of these phasor notations as a powerful tool used to define electric power. In order to evaluate AC power, one needs to usually find the product of voltages and currents, because by definition power is: p tv ti t () = × 6-1
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L302-6.5 As will be seen in the next section, various types of power exist and we will try to define and differentiate them from one another. Background Information As you shall learn during this lab: there are various types of power. Example of these are: instantaneous, average, real, reactive, total, apparent, etc. We shall analyze several of these different types of power and attempt to clarify the differences between them. a) Instantaneous power . Consider a linear network which has steady-state currents and voltages, periodic functions in time (both of period T ), as inputs. The outputs will also be currents and voltages which are also periodic functions in time. Instantaneous power is defined as below, p tv ti t () = × In this definition it is noted that instantaneous power is a function of time and also periodic (but not necessarily of period T ). Note: whatever the fundamental period of p(t) is, let us denote this as T p , T must contain an integral number of periods of T p. b) Average power. Consider the above definition of instantaneous power. Two things stand out: (i) The time varying nature of p(t) and (ii) the periodic nature of T. So to present average power, there is a need to evaluate an average value of p(t). The averaging so to say must be performed over a period of interest. The question now is over what period? T p or T. To answer this, look at the following relationship: P T ptd t T t p t tT p t == ++ ∫∫ 11 1 1 1 1 P is average power. From this we can see that it doesn’t matter whether or not we use T p or T just as long as make the corresponding necessary changes in the limits of the integral.
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- L302-6.5 Drexel University Electrical and Computer Engineering Dept Electrical Engineering Laboratory II ECE L 302 C O Nwankpa Measuring AC

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