Question

a) Two resistanceless rails rest 23 cm apart on a 6.0∘ ramp. They are joined at the bottom by a 0.50 Ω resistor. At the top a copper bar of mass 0.030 kg (ignore its resistance) is laid across the rails. The whole apparatus is immersed in a vertical 0.85 T field. What is the terminal (steady) velocity of the bar as it slides frictionlessly down the rails?

b) Design a dc transmission line that can transmit 975 MW of electricity 245 km with only a 2.5% loss. The wires are to be made of aluminum and the voltage is 680 kV . The resistivity of aluminum is 2.65×10−8Ω⋅m. What should be the minimum transmission line diameter.

Answer 1

soln 7 B (2) L=23cm = 23m R=0.5 m= .030kg B=0.85T mgsino дала - o= 6 N TB. FB Cso AL mgsino ingcoso zero. v= let terminal speed is ve induced emf &z VBL 2 P = E/R = (URL) magnetic Fuste FB = ÜBL Fo. = FB = 3= (VBL JBL mgong Fio terminal velocity Net force is = mgsino = 9 = FB Caso mg sino = V BL? Csoy U= mgr tano B²L2 0.0 30x9.8X0.5 x tan(6) (0.85) 2 (123)2 = 0.4042 m/s terminal speed= 0.4042 mis (b) power p= 975 MW= 975X106W, V= 680 KV i= b AR=V. 680x103 P Resistance = 680x680 X103 x103 = 474.25642 9758106 R= fli R=fe. (d=diameter xd2 4 (481 4x 2.65/10-8X245X103 RA 474.2564XT d= 4.17498x103 m= 4.17498 mm 9758406 I Ā diameter