Question

6. You and a friend rent a room in an old house and find that if both of you are using your blow dryers, the 20 amp fuse for that circuit occasionally blows. Each blow dryer has a high and a low power setting, which has the effect of fixing the electrical resistance. The wire from the fuse box is as old as the house, and has an additional resistance which newer wiring would minimize. W 120V 120V Powerline R2 20A Fuse Equations for the current flowing through each element of the circuit are obtained from Kirchhoff's laws. The first equation states that the current flowing through the wire goes into one or the other blow dryer, so that where W refers to the wire, while 1 and 2 refer to the blow dryers. Two additional equations result from the fact that for any loop of the circuit, the voltage dissipated by resistors must equal the source voltage. Thus, RiRi V RiRi = V Where . K and 2 are the resistances andVis the voltage (120 volts). (a) Write this system of three equations in matrix form AB = X ,where X is a column vector whose entries are the three unknown currents. (b) Solve this matrix equation for the currents when both blow dryers are in use. Consider three cases: both blow dryers operating at low power; both at high power; and one on low and one on high. Let the two power settings be 1000W and 1500W, for which the associated resistances are 152 and 102 , respectively. (Note that higher resistance reduces the power drawn by the dryer.) In all cases, let the wire resistance be R = 0.552 Can both blow dryers be used simultaneouslyynder any conditions? Under what conditions will the fuse blow?

Answer 1

a.) V wiwti,V V Rwi V Rz12 =V Rwx O (RNt ,)x gires -R1 + RIV l2 Rw (R,tR),R rmO R2 V V hu(Rith2t,2 Rwth Rw(R,t2)+h,8

9n matrixf V Ryth2 R'2 V LW A b) Case 1. both o bouu R D Sn 36X120 2102 3o x 20 A - D SX30+ 225 high baneu bo th lase 21.8 A 20 X12 20 x120 0.S x20 td iphbonc at Cas oT X ST 8.4 A 0-S X2S 1So mou than 20 A , So ^usc hill blow. Honeru Case lm han 20A tam buud ainultancouly . dizenn CS