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1 Name: Sigature Date: (Prit ECE Quiz # S.. Brakoic Sectio W :30 A October, 00 KEEP THIS QUIZ CLOSED AND FACE UP UNTIL YOU AE TOLD TO BEGIN.. This quiz is closed book, closed otes. You may use oe 8. crib sheet, or its equialet.. Show all work o these ages. Show all work ecessary to comlete the roblem. A solutio without the aroriate work show will receie o credit. A solutio which is ot gie i a reasoable order will lose credit. If your work cotiues o to aother age, idicate clearly where your work ca be foud. Failure to idicate this clearly will result i a loss of credit. 4. Show all uits i solutios, itermediate results, ad figures. Uits i the quiz will be icluded betwee square brackets.. Do ot use red ik. Do ot use red ecil. 6. You will hae miutes to work o this quiz. /00 %
2 Problem #. Imagie the situatio where you are at your home, let say, doig your hobby roject. You hae a broke multimeter which you wat to fi. You kow the rage of this multimeter from the origial maufacturer secificatio. If coected i arallel to the circuit oer termials A ad B it ca measure oltages u to 0 mv. Whe used as a ammeter the maimum rage is 30mA. You also kow that essetial art of this multimeter, the real d Arsoal meter hidde iside of the deice is workig fie ad has the maimum rage of ma ad/or 0mV. The desig of the multimeter is such that the eteded rage of this multimeter o termials A ad B is achieed by haig the certai umber of idetical resistors,,,,.. -, i arallel to d Arsoal meter. The same umber of these idetical resistors is coected i serial to this arallel coectio as well (see Figure. I order to fi your multimeter ad restore its ability to hae measurig rage of 0mV ad 30mA you eed to fid: a what is the origial umber of resistors (, b what is the alue of resistace.(note, that,, - c I additio to that, your fried has asked you to use this meter ad he asked you to sketch for him the multilyig factor of ammeter ad oltmeter as a fuctio of the umber of resistors, assumig the origial alue. Figure.
3 Solutio: This is a easy but little tricky roblem. Let s hae a careful look to the tet ad Figure. If we hae doe that, we ca see that we ca simlify our circuit if we relace all resistors i arallel coectio with meter by their equialet resistace; EQ ;(.. EQ EQ ( The same ca be doe for the resistors coected i serial, EQ ;(.. EQ ( Also, it is straightforward to fid d Arsoal meter s resistace usig Ohm s law ad its maimum measurig rage; [ mv ] [ ma] 0 0 (3 Now, the circuit looks little simler (Figure ; Figure. Simlified ad labeled circuit from Figure. If we coect this multimeter i serial to the ossible circuit oer termials A ad B, the curret from the circuit I t will be slit oer the arallel coectio o the curret ruig through d Arsoal meter I ad the curret ruig through the resistors i arallel I ( EQ /. Usig the curret diider rule, or the formula for the eteded rage ammeters we ca write eressio for curret I t as: 3
4 [ ] + 0 Ω + EQ I I I t (4 EQ Substitutig alues for curret I as the maimum measurig curret of d Arsoal meter (ma ad for I t the maimum measurig curret of our multimeter (30mA we get: ma ma, ( Obiously this ratio does ot gie us a elicit solutio for ad, ad we eed a additioal equatio i order to get this aswer. Let s look the oltage AB that would be o the termials A ad B if our multimeter is coected i arallel to some ossible circuit. The oltage AB will be diided o the oltage across the resistors i serial coectio s ( EQ ad oltage o the termials of the arallel coectio. Usig the oltage diider rule or eressio for eteded rage oltmeter we ca write: AB (6 + ( EQ ( EQ EQ + ( 0 ( 0 Substitutig alues for as the maimum oltage of d Arsoal meter (0mV ad for AB the maimum oltage of our multimeter (0mV we get: 0 + 0mV 0mV 0 (7 0 Ad combiig (7 ad ( we get; + ad 0 4
5 Now, sice we eed to sketch the multilyig factor deedece o for our oltmeter ad ammeter, usig 0[Ω], form equatio (4 ad (6 we get; I I t AB +, + + The grahical resetatio is show below: 3 30 factor 0 0 ab/ It/Im
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