Question

5. A rectangular coil of length a and width b consisting of N turns is rotated at a frequency fin a uniform magnetic field as shown in the Figure. The coil is connected to two co-rotating cylinders against which metallic brushes make a sliding electrical contact. This is the basic design of an alternating current generator. (a) Find the emf, E, induced in the coil as a function of time in terms of B, N, a, b, and f. (b) Design a loop that will produce a root-mean-square emf of 120 V when rotated at 60.0 revolutions/s in a field of 0.5 T. This time dependent emf is equivalent to that of a wall socket in your home. KX

Answer 1

Solution ohen the ceil 9totales, magnetic a changes y NBA cos (wt') AAua (t)= aft) 中 (t) = Ne ab Ce Neusy Faraday's law, ) Tnduced, Emf E= -dd dt (NBab caexft) Cos dt € (t) 2NB ab sin(2xft) Eo sin (2xft) E lt)

(b) Nous Square Emf Mean ERMS 20 V nad/s 60x 2 T Magnetic field, B 0.5T Now 27NBab MS 2 2 (60) N 0 S) ab 20 x2 Nab o.9 2K (ox0.S Nab o.9 m lp whose have to design pro du ct of number of tuons and we area Cab) is 0.9 One such design is, N = Io twins lenyit 0.3 m width 0 3 m