Determine flux in the central limb:

For the magnetic circuit shown in Figure the value of flux in the right limb is 0.48 m Wb and the number of turns wound on the central limb is 1000. Determine (a) flux in the central limb, and (b) the current needed.

The magnetiSation curve for the core is specified as below:

Figure

Solution

Area of cross-section in side limbs = 4 × 3 =12 cm²

Area of cross-section in core = 4 × 3 = 12 cm²

Flux in side limbs = 0.48 m Wb

Flux density in side limbs = (0.48 × 10)/ (12 × 10^{- 4})

                                               = 0.4 Wb/m²

For the flux density of 0.4 Wb/m², H = 200 AT/m

Since the coil is wound on the central limb and the magnetic circuit is symmetrical, flux in the central limb = 2 × 0.48 = 0.96 m Wb.

Flux density in the central limb = 0.96 × 10/12 × 10^{- 4} = 0.8 Wb/m²

For the flux density of 0.8 Wb/m², H = 400 AT/m

Side limb contain a path of length 50 cm. Central limb contain a path of length 20 cm.

Total m.m.f required = H× length = 200 × 50 × 10^{- 2} + 400 × 20 × 10^{- 2} = 180 AT

Current required =180/1000 = 0.18 Amp .