UCF PHY 2054C - Unit 14 - Coils and The Inductor

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[COILS & THE INDUCTOR -]STUDIOPHY 2054 College Physics IIDrs. Bindell & DubeyJanuary 14, 2019This experiment involves looking at inductors, coils and inductor time constants.PART I – INTRODUCTORY CONCEPTSIn the last unit we discussed induction (Faraday’s Law) and Lentz’s Law. We also recognized theimportance of Magnetic Flux in these studies. The next step is to study the last electric elementthat we will encounter in this course: the Inductor. The inductor has a property associated with itthat is called “inductance” and in this unit we will study its properties.The inductance of an inductor is referred to by the letter L which is added to our lexicon thatalready contains R and C. In this unit we will study the RL circuit (similar to the RC circuit) andthen we will plunge into AC circuits and the combination of all three elements.The symbol for the inductor is:We begin with some review questions:1) Consider a U-shaped metal rod with a metal rod touching it, which is free to slide (shownbelow). A magnetic field is into the page everywhere, as in the diagram. If the rod is moving to the right at a velocity v,2 | P a g e(i) Would there be a current? Explain. If so, determine the direction of the current.(ii) Would there be an emf? Explain. If so, calculate the emf in terms of the magneticfield, B, the velocity of the rod, v, and the length l. (i.e. tDFD)2) Two solenoids 1 and 2 are sufficiently close together that the magnetic field formed insolenoid 1, in the presence of electric current, also penetrates into solenoid 2.3 | P a g ea) If the switch is closed so that a steady current is present in solenoid 1, what is the direction ofthe magnetic field in solenoid 2? Show its direction by means of an arrow in the diagram.Explain your result. If the B-field is zero, say so explicitly and explain your reasoning.b) If the switch is now opened, and the current in solenoid 1 drops to zero, describe what, ifanything, happens in solenoid 2, showing the direction of any current induced in solenoid 2.Explain your reasoning. Is there a current in solenoid 2 after the current in solenoid 1 hasdropped to zero? Explain your reasoning.3) The diagram shows a circuit with a variable resistor on the right and a closed wire loop on theleft. 4 | P a g eSuppose the lead is slid to the right, increasing the resistance. Will there be a current induced inthe wire loop on the left? If so, in what direction? If not, why not? Explain your reasoning.We just discussed the subject of inductors in class so let’s do some thinking about how theywork. Consider the coil shown below:All coils have some built in resistance so assume that this coil has some as well. The resistancecan be taken as R ohms and the current is I. If the current is steady, what is the voltage dropacross the coil?NOTE: We will be using the coil on the RLC experimental board; the value of its resistance R is listed under the photograph.5 | P a g eThe specifications for the coil are:Inductor: - 8.2 mH @ 1 kHz, 6.5 Ω maximum DC resistance, 0.8 A current rating RMS, 3/4" I.D. x 1-3/4" O.D.The current through the coil produces a magnetic field in the coil given by 0B nim=where n isthe number of turns per unit length. Is there a magnetic field in the coil (steady current) and if so,which way does it go? (Sketch your assumed coil winding directions). If not, why not?[Remember to refer to the diagram as you answer these questions.]Suppose now that the current begins to increase. As it does so, the flux through all of the coils isincreased. The increasing flux causes an induced current in the windings. What is the directionof the magnetic field that this increased flux induces?6 | P a g eRemembering that there is an electric field associated with the induced current (in the wire), howdoes the direction of this emf compare with the emf driving the current itself (from a battery orpower supply)?What is the electrical effect of this induced voltage on the total voltage on the coil?The total “back emf” can be expressed asiemf LtD=Dwhere we have omitted the sign. L is the inductance of the coil and is measured in Henrys (H).Consider the following question:The current through a 3.8 mH inductor varies with time according to the graph shown in the drawing. What is the average induced emf during the time intervals? Region I: __________ Region II: __________ Region III: __________Compare your answers with other groups and resolve any discrepancies. 7 | P a g eConsider the following series LR circuit:With the switch open, no current flows. As the switch closes, the potential across the inductorsuddenly increases so the back emf is a maximum. The current therefore starts at zero and willbuild.What is the MAXIMUM current that the circuit will carry when the t (time) gets very large?ANS: _____________We therefore expect that this circuit will increase its current until the current reaches itsmaximum value. How long do you think this will this take?ANS: _____________secondsIf we look at the circuit we see that we can write Kirchoff’s loop law as:0tiLiRThis is called a differential equation and it requires some calculus to obtain a solution. Skippingthis step, we can write the solution as:8 | P a g e    constanttime11Solution//RLeRieRittLRNotice that the first factor ε/R is the maximum current that the circuit will achieve, we cannormalize this equation so that the maximum current is unity:/(1 )tnormalizedi et-= -where --is the time constant. There are three resistors on the board but only one inductor. What is the time constant for each resistor that we can place in the RL circuit?10- _______________ 33-_________________ 100-----------------Using your calculator, plot the normalized current vs. time for a time span of 4 time constants.Do it for the 33- as well as 100- resistors. Compare your results. After how many time constants is the current effectively at a maximumvalue?9 | P a g eAfter how many time constants is the current essentially constant?Estimate is the time constant for the following graph?ANSWER -=_______ secondsHint: What is the value of the function when t=-?Now consider the following circuit:10 | P a g eFollowing the same process as before, when the second switch is closed, the current will begin todrop off but the induced current will slow


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UCF PHY 2054C - Unit 14 - Coils and The Inductor

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