Question

The two coils A and B wound coaxially on an insulating cylinder. It will be evident that the fluxes produced by a current i through the two coils are in the same direction, and the coils are said to be cumulatively coupled. If the direction of the current in B relative to that in A is reverse, then coils are said to be differential coupling. Suppose A and B to have self- inductances LA and LB henrys respectively and a mutual inductance M henrys. If two coils are connected in series, their effective inductance is found to be 12.0H. However, when the connections to one coil are reversed, the effective inductance is 8.0 H. If the coefficient of coupling is 0.6. a) Show that the total inductance of inductively coupled circuits is LA + LB 2M CR (5) b) Calculate the self-inductance of each coil and the mutual inductance. EV (7) (c) A mild-steel ring having a cross-sectional area of 500 mm2 and a mean circumference of 400 mm has a coil of 200 turns wound uniformly around it. Calculate: a. the reluctance of the ring; b. the current required to produce a flux of 800 je Wb in the ring.

Answer 1

Part (di It is given that; Area, A= 500 mm² and a mean of cumference (l)= 400mm with Number of Lund, N= 200 9) The reluctance of the ring : R= l here do A do = 478107 Him = > R= 014 407X1674015X102 636.9 x les Amp R turn/Weber b) for The Cument , magnetic flux , B = 800 de Wb relation between Current(l) and Magnetic flux (B) is Ja IB lon 400x10²x Booxlo I = [ N = 200 given 40 X 10.7 x 200 I = 1.273 Amp