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.

An inductor is constructed by winding a coil of 100 turns around a magnetic core. The core is a cylinder with radius 0.5 cm and the core material has relative permeability of 1000. The coil covers a length of 10 cm. Determine the resulting inductance. Enter your answer in mH rounded to two decimal places.

A flux of 0.0016 Wb flows in a silicon sheet steel coil/core. The arrangement appears as shown below with the following dimensions: Ac = 0.0025 m? Core/gap area: Flux path length: le = 0.350 m lg = 0.0015 m N = 500 Air gap length: Number of turns: %3D A. What is the current, I, through the winding? B. What is the energy stored in the inductance? C. Assume that the current is given by i =9.75 sin (3147) A. What is the RMS voltage that would appear across the winding? D. Assume that the gap is removed from the arrangement with the flux path remaining at 0.350 m. For a flux of 0.0016 Wb, what is the inductance of the arrangement? E. What is the energy stored in the inductance with the gap removed?

An air-cored choke is designed to have an inductance of 20H when operating at a flux density of I Wb/m²: the corresponding relative permeability of iron core is 4000. Determine the number of turns in the winding: given that the flux path has a mean length of 22 cm in the iron core and I mm in air gap and that its cross-section is 10 cm².