Answer to Question #114234 in Electrical Engineering for Kwesi

Question

A cast steel frame is to be used as the core of an inductor.



An 800 turn coil is wound on the centre limb of the frame which has two similar outer limbs in parallel with each other.

The frame has the following parameters:

Outer limb: c.s.a. of 2000 mm2 and length of 700mm.

Centre limb: c.s.a of 4000 mm2 and length of 250 mm.



Determine the coil current to set up a flux of 1mwb if a saw-tooth (an air-gap) of 1mm is cut in the centre limb.



The relative permeability of steel is 1000.

Answer 1

Gap length: $L_g=0.1\text{ cm}.$

Core length: $L_c=70\text{ cm}.$

Core area: $A_c=20\text{ cm}^2.$

Gap area: $A_g=40\text{ cm}^2.$

Central limb length: $L_l=25\text{ cm}.$

Calculate the magnetic reluctance:

$$R_c=\frac{L_c}{\mu_0\mu A_c}.\\ \space\\ R_g=\frac{L_g}{\mu_0\mu A_g}.\\ \space\\ R_l=\frac{L_l}{\mu_0\mu A_g}.\\ \space\\$$

The magnetic circuit can be calculated like electric circuit, but with flux instead of current and with magnetomotive force instead of voltage:

$$\Phi_g=\frac{NI}{R}=\frac{NI}{R_C/2+R_l+R_g},\\ \space\\ I=\frac{\Phi_g}{N}(R_C/2+R_l+R_g)=0.24\text{ A}.$$