PHYS-115(x) (Kaldon-xxxxx) Name ______________________________________________WMU - Fall 2006Exam 3 - 100,000 points Book Title __________________________________________Section: 3a 3b 3c 3d Sample Exam A to F G to M N to S T to Z 11/16/2006State Any Assumptions You Need To Make -- Show All Work -- Circle Any Final AnswersUse Your Time Wisely - Work on What You Can - Be Sure to Write Down EquationsBOLDFACE Variables Are Vectors - Feel Free to Ask Any QuestionsThe Light Bulb and The Room Problem (25,000 points)1.) If you look closely at the filament in most light bulbs, you’ll see that the wire is usuallycoiled. If the filament is coiled, then the coil must have an inductance. (a) Find theinductance, L1, of the light bulb, given that the filament is 1.00 cm (0.0100 m) long, has adiameter of 4.00 mm (0.00400 m) and has 15 turns.(b) This is a 25 W light bulb, that is it dissipates 25 W of power from its resistance. For V = 125 Volts, find thecurrent, i, and resistance, R, of the light bulb.(c) Find the energy, UL, that the inductor L1 can hold in its magnetic field, with the current i.(d) Although the inductor is made up from the very wire that forms the resistor, we can consider R and L1 to bein series. Find the time constant of the light bulb. Will it make any difference in how long it takes for the bulbto light? Do you have to state any other assumptions in this part?(e) Suppose this light bulb in a room is wired so that the current carrying wire makes a big rectangular loop,3.00 m x 5.00 m. Find the inductance L2 of this loop. L1 and L2 will be in series. Which inductance has thebigger impact on the circuit?Physics 115 / Exam 1 Winter 2001 Page 2Mutual Self-Admiration Society Meeting (25,000 points)2.) A current i = 1.00 A flows through a 400 loop inductor, L1 = 44.4 mH. (a) Find the flux FB of the magneticfield inside.(b) Do you have enough information to find the magnitude of the B-field given FB from (a)? To find the B-field using the solenoid equation? In each case, either state what else you’d need to know or find B.(c) If the current was suddenly introduced into the inductor L1 in 0.0100 s, find the self-induced emf. (d) Nearby there is a second inductor, L2 = ½ L1. If L2 has only 200 loops, find the mutual inductancecoefficient, M, between the two coils and the emf induced in L2 by the current i1 from (c).(e) If these two coils were part of a transformer, and the primary (L1) voltage was 110 V 60 cycle A.C., whatwould be the voltage on the secondary side?Physics 115 / Exam 1 Winter 2001 Page 3“Phasors Set on Stun, Captain!” (25,000 points)3.) An RLC circuit contains the following elements: R = 1000 W, C = 1000 pF and L = 1000 mH. It is drivenby an AC generator with w = 377 rad/s. (a) Find the capacitive and inductive reactances, XC and XL.(b) Find the impedance, Z, for the circuit. For what value of w is the impedance a minimum?(c) If the vector in the phasor diagram on the left represents IL, sketch in VL and show the relevant instantaneouscomponents, iL and vL. Don’t worry about the scales of the graphs.(d) If the vector in the phasor diagram on the right represents IR, sketch in VR and show the relevantinstantaneous components, iR and vR. Two light rays hit an air-glass boundary at q = 60°. Make your calculations and show on the diagram whathappens to the refracted and reflected rays of (d) the light ray coming from the air and (e) the light ray comingfrom the glass.Physics 115 / Exam 1 Winter 2001 Page 4Power to the People! (35,000 points)4.) (a) Two parallel power lines each carry 480. A of current in the same direction. If the cables between twopower poles are 85.0 m long and are separated by a distance of 3.50 meters, find the magnetic force between thetwo power lines, and indicate whether they are attracted or repelled. For simplicity’s sake, treat this as D.C. inthis part, even though we know that the power lines are really A.C.(b) At the house of a mad scientist, Dr. Fyl, the 480. A is used at 118V A.C. to power his cathedral of Micron Millennia Pentium computers. The power plant is 25.0 km away, and50.0 km of wires (to and from) has a total resistance of 22.5 W . If 480. A runs through the wires, find theefficiency of this power distribution system.(c) If instead, the electricity is set at 118,000 V A.C. on the power lines, find the new efficiency of the powerdistribution system. (d) The voltage is changed by a step-down transformer from 118,000 volts to 118 volts. The secondary coil hasN2 = 1000. turns. How many turns does the primary loop have?(e) Our transformer is sketched below – note that both sides have the same number of turns so as not to suggestan answer for (d)! If at some time t0 that the primary current I1 is increasing and going to the right as shown,then explain whether the induced current of the secondary, I2 , goes to the LEFT or to the RIGHT.Physics 115 / Exam 1 Winter 2001 Page 5“Care For Some Toast?” THE TOASTER IN THE BBC TV SHOW RED DWARF (35,000 pts.)5.) (a) A toaster generates Joule heating at a rate of 855 W when plugged into a125 volt D.C. power source. This results in a current of I = 6.84 A. Thenichrome wire used in the heating element is a high resistance wire, but still theentire heating element only has a resistance of R = 18.3 W. The heating elementcan be unfolded to be a single coil 0.500 cm in diameter and 45.0 cm long, with480. turns. Find the inductance, L, of this coil.NOTE: If you do not get an answer to (a), use L = 252 mH in parts (b) - (e).(b) If this toaster into an AC wall outlet, with Vrms = 125 volts and f = 60.0 Hz, find the inductive reactance, XL,of the heating element.(c) Sketch a single phasor diagram showing vR , vL ,and the current, i .“In Use” Equation “By Geometry” EquationRVIR=RLA=rCQCV=CAd= e0(Parallel Plate Capacitor)LLNIB=FLNAl=m02(Air-Core Solenoid)(d) The heater element can be thought of as being a resistor and an inductor in series. What is the time constantof this RL circuit?(e) Use the impedance to find Imax for the toaster. There is no capacitive nature to this circuit.Physics 115 / Exam 1 Winter 2001 Page 6Fish Stories (50,000 points)6.) (a) A fish lives in fresh water, n = 1.33, in a fish tank madeof glass, n = 1.50, that has an acrylic coating on the inside, n =1.25. The fish tank is lit with a sodium light, whose wavelengthin air is l = 555 nm = 5.55 × 10-7 m. If the acrylic coating is ahalf-wave