Question

1. Consider the toroidal core shown in the Figure. Find the current needed to produce a flux density of BFe = 1.2[T] in the following two case - No air gap - With a 2-mm air gap Let N = 100 and u = 4000 for the iron. The iron cross-sectional area, A = 4cm.

Answer 1

Toroidal Core:

Toroids are commonly used for current and instrument transformers, where low losses are extremely important. When comparing with conventional transformers where the core losses total 50% of the total power loss, the advantages are easily seen.These toroidal cores are wound by automatic core winding machine and are annealed in high vacuum furnace under protected atmosphere or in continuous tunnel furnace, which results in features like compact volume, light, low magnetic leakage and hum & high efficiency.

In the above problem,

Given dalay N: 100 = 320 mm u= 4000 t for ison) Azea 4 tm 4 x(10) m A BEE X 1-2 4. X 104 %3D FE The relueläuce %3D 32a x10 At /wb 6a x 105 given lag, FE R homs Ampers Ala, NI = 100 0.769 A and air gap, path Seperatng the Rahae tame Apr inen (izon) Rre %3D 3. 320 X 10 yo00 x 4Ti 1 loxu X16 At/wb. 1.592 X 10 (air) 2 Y10 Rair Rair = 39.71 x15 the to tal uluctaue Riobl Ree + Rair %3D

Rtot 1.592 X 15 + 39.79 x 10 %3D Rtot 4 1.38 X1o5 Also, NI= OFE Rtot I= OFE R tot 769x xo X 41.38 XIO 48x105 100 I= 19.86 A Cursent

Answer : The current needed to produce the flux is 19.86 A